Exam 3: binomial relationships

In binomial methods, does categorical data contain more information than continuous data? No, continuous data can be ranked and has more possible values. Yes, categorical data contains more information than just a number. Yes, categorical data contains all the information about the category. No, continuous data can be normally distributed.

No, continuous data can be ranked and has more possible values.

In binomial methods, does binomial data contain more information than categorical data? No, because binomial data has only two possible values. Yes, because binomial data is numerical. Yes, because binomial data is a special case of categorical data. No, but binomial methods can pull out more information.

No, but binomial methods can pull out more information.

In binomial methods, can binomial data be two textual words? No, binomial data must be categories, not words. Yes, binomial data is any data with only two possible values. No, binomial data must be the numbers 0 or 1. No, binomial data can be any two possible numerical values.

No, binomial data must be the numbers 0 or 1.

In binomial methods, if continuous data values contains more information, why are methods for binomial data important? They are more effective methods in the presence of extreme values. They make the data easier to work with by dropping to two data values. All of these other answers. They give partial information when continuous data values are hard to get.

They give partial information when continuous data values are hard to get.

In binomial methods, what is a binomial event? One trial of a binomial situation. One flip of a coin. One question with a yes/no answer. All of these other answers.

All of these other answers.

In binomial methods, what is the importance of a binomial event? It sets up the use of more advanced binomial methods. It converts continuous data into binomial data. It is the atomistic level of a binomial situation. It allows the conversion of non-numerical data into numerical data.

It allows the conversion of non-numerical data into numerical data.

In binomial methods, what is a binomial experiment? A test to determine if the data values are binomial data values. A binomial event that is repeated over and over. A fixed number of binomial events with the outcome being the number of successes. An experiment designed to have only two possible outcomes.

A fixed number of binomial events with the outcome being the number of successes.

In binomial methods, what are the two advantages to analyzing a binomial experiment over a binomial event? Gives a larger sample size. Gives sample data values closer to population data values. Converts binomial data into discrete data. Results in a histogram for calculating probability.

Converts binomial data into discrete data. Results in a histogram for calculating probability.

In binomial methods, if the number of successes from a binomial experiment is known to be distributed binomially (BIN), what other information is needed to be able to calculate probability (these are called the critical parameters)? The number of trials (n) in the binomial experiment. The population standard deviation (σ) of the number of successes. The probability (p) of getting a successful outcome. The population mean (µ) of the number of successes.

The number of trials (n) in the binomial experiment. The probability (p) of getting a successful outcome.

In binomial methods, is the normal curve a good enough approximation of the binomial histogram to get probability for every binomial situation? All of these other answers. No, only when the equation 10≤np(1−p) true. No, the condition to use the normal approximation must be met. No, only for a large enough sample size or a probability of success close enough to 0.5.

All of these other answers.

In binomial methods, what are the critical parameters for a normal curve? n and p. b0 and b1. µ and σ. ¯¯¯x and s.

µ and σ.

In binomial methods, if the critical parameters of a binomial distribution are n and p, what two choices below show how the critical parameters (µ,σ) of the approximating normal curve is found? σ=√np(1−p). σ=(∑pn−1). μ=np. μ=∑pn.

𝜇 = 𝑛𝑝 𝜎 = √[𝑛𝑝(1−𝑝)]

In binomial methods, in the blanks of the schematic normal curve, what is the difference between a normal x-value and a binomial b-value? x-value is a number, b-value is a number. All of these other answers. x-value is a number, b-value is a number and an inequality sign. x-value is continuous, b-value is categorical.

x-value is a number, b-value is a number and an inequality sign.

In binomial methods, why is there a need for the continuity correction? To keep the numbers continuous when going through the method. To correct for an inherent bias in binomial data. To eliminate any gaps in the binomial histogram. To change from finding area under bars (have width) to areas under lines (no width).

To change from finding area under bars (have width) to areas under lines (no width).

In binomial methods, how is the method of the continuity correction done? Using a table and the degrees of freedom to find the value of the continuity correction. Multiplying or dividing by 0.5 to correct for the different levels of measurement. Adding 0.5 to correct for area lost in the far-left tail of the normal curve. Add or subtract 0.5 to start measuring area from one side of the histogram bar.

Add or subtract 0.5 to start measuring area from one side of the histogram bar.

In binomial methods, which variable(s) in the data set shown below contain binomial data? Height Speed Salt Vote Tall Fast 0 0 Short Slow 2 1 Short Slow 2 1 Tall Fast 0 0 Variables Salt and Vote, contain two values of numerical data. All variables, contain two values of data. Variables Height and Speed, contain two values of textual data. Variable Vote, contains two values of 0 and 1.

Variable Vote, contains two values of 0 and 1.

In binomial methods, select the choice below that is an assumption for a binomial event? All of these other answers. Each result is recorded as 0 or 1. Each event has the same probability of success. Each outcome is independent of all the other outcomes.

All of these other answers.

In binomial methods, why are the histograms of binomial events / the probabilities of binomial events, not overly interesting in the science of statistics? The histograms have gaps / cannot calculate area in only one bar. A scatterplot is a better graph / cannot find the regression equation. The histograms only contain two bars / can only get probability of success. The histograms are bimodal / cannot use the z-Table.

The histograms only contain two bars / can only get probability of success.

In binomial methods, why are the histograms of binomial experiments / the probabilities of binomial experiments, of much greater interest in the science of statistics? The histograms can be skewed / probability is more interesting to get. None of these other answers. The histograms have the normal shape / probability is easier to get. The histograms contain many bars / can get the probability of many events.

The histograms contain many bars / can get the probability of many events.

In binomial methods, why are the number of trials (n) and the probability of success (p) the critical parameters of binomial experiments? They are critical for the publishing of the results of binomial experiments. They are part of the assumptions of binomial experiments. They are needed to calculate probability with the binomial equation. They are needed for the proper interpretation of binomial experiments.

They are needed to calculate probability with the binomial equation.

In binomial methods, what does the phrase Normal Approximation to the Binomial mean? A way to approximate binomial data with normal data. A method to approximate the degrees of freedom in a binomial experiment. A simple approximation easier to use than more advanced approximations. To use a normal curve to approximate the area under a binomial histogram.

To use a normal curve to approximate the area under a binomial histogram.

In binomial methods, can a normal curve be used to approximate the area under a binomial histogram for all binomial situations? No, a normal curve cannot approximate a histogram with two bars. No, only when the binomial histogram is unimodal and symmetrical. No, only for histograms with 30≤np(1−p). No, only histograms with high, or low, probability of success.

No, only when the binomial histogram is unimodal and symmetrical.

In binomial methods, use the information below to calculate the value of the mean / the standard deviation, of the appropriate normal curve to use to find probability for this binomial situation? n = 60; p = 0.45 µ = 27 / σ = 14.85. µ = 27 / σ = 3.85. µ = 27 / σ = 0.45. µ = 30 / σ = 5.19.

µ = 27 / σ = 3.85.

In binomial methods, use the information in the table below to find the continuity corrected value for Situations A / B / C / D? Situation Probability A Less than 11. B Less than or equal to 10. C Greater than 10. D Greater than or equal to 11. 10.5 / 10.5 / 10.5 / 10.5. 11.0 / 10.0 / 10.0 / 11.0. 11.5 / 10.5 / 10.5 / 11.5. 11.0 / 11.0 / 11.0 / 11.0.

10.5 / 10.5 / 10.5 / 10.5.

In binomial methods, the state police estimate that 35% of highway drivers speed over 80 mph. If 100 highway drivers are stopped, what is the probability that more than 40 of them were speeding over 80 mph? (np(1-p) = 22.75)? Probability = 0.1251. Probability = 0.1736. Probability = 0.8264. Probability = 0.8749.

Probability = 0.1251.

In binomial methods, the state police estimate that 35% of highway drivers speed over 80 mph. If 100 highway drivers are stopped, what is the probability that 40 or more of them were speeding over 80 mph? (np(1-p) = 22.75)? Probability = 0.1736. Probability = 0.8749. Probability = 0.1251. Probability = 0.8264.

Probability = 0.1736.

In binomial methods, a dentist estimates that 75% of people don't floss enough. If 100 people are selected , what is the probability that more than 70 of them don't floss enough? (np(1-p) = 18.75)? Probability = 0.1020. Probability = 0.8508. Probability = 0.8980. Probability = 0.1492.

Probability = 0.8508.

In binomial methods, a dentist estimates that 75% of people don't floss enough. If 100 people are selected , what is the probability that at least 70 of them don't floss enough? (np(1-p) = 18.75)? Probability = 0.1020. Probability = 0.8980. Probability = 0.8508. Probability = 0.1492.

Probability = 0.8980.

In binomial methods, a veterinarian estimates that 40% of people don't have their dogs vaccinated. If 100 people are selected , what is the probability that less than 30 of them don't have their dog vaccinated? (np(1-p) = 24.0)? Probability = 0.9838. Probability = 0.9738. Probability = 0.0162. Probability = 0.0262.

Probability = 0.0162.

In binomial methods, a veterinarian estimates that 40% of people don't have their dogs vaccinated. If 100 people are selected , what is the probability that 30 or less of them don't have their dog vaccinated? (np(1-p) = 24.0)? Probability = 0.0262. Probability = 0.9738. Probability = 0.0162. Probability = 0.9838.

Probability = 0.0262.

In binomial methods, it is known that 70% of women wear lipstick of some type of red color. If 100 women are asked , what is the probability that less than 75 of them wear lipstick of some type of red color? (np(1-p) = 21.0)? Probability = 0.8849. Probability = 0.1635. Probability = 0.8365. Probability = 0.1151.

Probability = 0.8365.

In binomial methods, it is known that 70% of women wear lipstick of some type of red color. If 100 women are asked , what is the probability that no more than 75 of them wear lipstick of some type of red color? (np(1-p) = 21.0)? Probability = 0.1151. Probability = 0.8365. Probability = 0.8849. Probability = 0.1635.

Probability = 0.8849.

In binomial methods, the proportion is to binomial data as what statistic / parameter, is to continuous data? The standard error of the mean / The standard error of the population. The sample size / The population size. The sample standard deviation / The population standard deviation. The sample average / The population mean.

The sample average / The population mean.

In binomial methods, the equation to calculate the sample proportion of binomial data is shown below. How is the value for x found? ˆ p = x/n It is given in the question. By using the z-equation. By summing the column of binomial data values. By using the Continuity Correction.

By summing the column of binomial data values.

In binomial methods, the equation to calculate the spread of the sample average of continuous data is shown below. What is the equation to calculate the spread of the sample proportion of binomial data? s¯x = σ/√n sˆp=np(1−p)√n. sˆp=√ˆp(1−ˆp)n. sˆp=ˆp(1−ˆp)√n. sˆp=√ˆp(1−ˆp)√n

𝑠𝑝ˆ=√[𝑝ˆ(1−𝑝ˆ)]/(√𝑛)

In binomial methods, what information is given by a confidence interval for the population proportion? The level of confidence in the estimated value of the population proportion. An interval of reasonable values for the population proportion. None of these other answers. The value of the population proportion.

An interval of reasonable values for the population proportion.

In binomial methods, out of 100 95% confidence intervals calculated from 100 separate random samples, how many of these confidence intervals should include the actual value of the population proportion? 95 The number differs for every new situation. Unknown, and cannot be determined ahead of time. Over 90.

95

In binomial methods, what value lies exactly in the middle of a confidence interval for population proportion? The value of the margin of error. The middle confidence limit of the confidence interval. The value of the margin of error multiplied by two. The value of the sample proportion.

The value of the sample proportion.

In binomial methods, what information is given by the margin of error of a confidence interval for population proportion? The spread of the sample proportion. The spread of the population proportion. Half of the width of the confidence interval. Twice the width of the confidence interval.

Half of the width of the confidence interval.

In binomial methods, the equation to calculate the margin of error for continuous data is shown below. What is the equation to calculate the margin of error for binomial data? ME = t ∗ (s/√n) ME=z∗√^p(1−^p)/n All of these other answers. ME=z∗√(ˆp(1−ˆp)/n) ME=z∗√(ˆp(1−ˆp)/√n)

ME = z ×√[p̂ (1−p̂ )/n]

In binomial methods, what is the critical value for a two-tail hypothesis test for proportion at a 90% level of confidence? CV = ±1.28. CV = ±1.96. CV = ±1.64. CV = ±0.83.

CV = ±1.64.

In binomial methods, select the two approaches below that are most used to make a conclusion in a hypothesis test for proportion? The confidence interval approach The p-value approach The critical value approach The F-value approach

The critical value approach. The p-value approach

In binomial methods, use the information below to find the value of the test statistic for a two-tail hypothesis test of proportion at a 95% level of confidence? np(1−p) = 37.5 ˆ p = 0.45; p = 0.5; n = 150 -1.22. -15.00. -2.45. +2.45.

-1.22.

In binomial methods, what is the proper conclusion to a hypothesis test using the information below? Do reject H0, as the test statistic is in the rejection region. Do not reject H0, as the test statistic is in the acceptance region. Do not reject H0, as alpha is greater than the p-value. Do reject H0, as the test statistic is less than zero.

Do not reject 𝐻0, the test statistic is in the acceptance region.

In binomial methods, a researcher wanted a sample from a population of people with equal numbers of the two genders. Giving the male the binomial value of 1, what is the proper interpretation of the conclusion to Reject the null hypothesis using the hypotheses shown below? H0 : p = 0.5; H1 : p ≠0.5 The population does not contain 50% males. The population does not contain 50% females. The population does not contain equal numbers of the two genders. All of these other answers.

All of these other answers.

In binomial methods, what characteristic of a distribution does proportion measure in a column of data values? The location of the data values. The count of the data values. The spread of the data values. The shape of the data values.

The location of the data values.

In binomial methods, what data values are appropriate to calculate the sample proportion? Any two numerical values, that are not equal. Any two data values, numerical or text. Only two data values, taken from binomial individuals. Only two numerical values, 0 and 1

Only two numerical values, 0 and 1.

In binomial methods, what does the word proportion of binomial data mean? The portion of 0's and 1's in the column of binomial data values. The portion of failures in a binomial event. The portion of successes in a binomial experiment. The portion of zero's in the binomial experiment.

The portion of successes in a binomial experiment.

In binomial methods, shouldn't area under the binomial histogram be approximated by area under the t-curve, since the population standard deviation is not given (normal condition is met)? No, the normal curve approximation is a better fit. No, it is not possible to calculate the correct degrees of freedom. Yes, when enough data values are in the column of data values. Yes, the t-curve approximation should be used in this situation.

No, the normal curve approximation is a better fit.

In binomial methods, a confidence interval for the population proportion is a situation with how many tail(s)? Always a two-tail situation (in this book). Always a one-tail to the right situation. Always a body area that does not have tails. Either a one-tail or two-tail situation depending on the question.

Always a two-tail situation (in this book).

In binomial methods, in a hypothesis test for population proportion, what information is used to make the null hypothesis / the alternative hypothesis? The current value of p / The researcher's value of p. The given value of p / The tested value of p. The actual value of p / The theoretical value of p. The theoretical value of p / The actual value of p.

The current value of p / The researcher's value of p.

In binomial methods, select the two choices that are true in the Happy Clown with Glasses memory device? The critical value is calculated from the test statistic. Alpha is divided by the number of tails to get the critical value. Area is multiplied by the number of tails to get p-value. p-Value is the area in the tail(s) from the critical value.

Alpha is divided by the number of tails to get the critical value.

In binomial methods, in the confidence interval for population proportion shown below, what are the values of the sample proportion / the margin of error? (0.65, 0.95) ˆP=Unkown/ME=0.15. ˆP=0.95/ME=0.30. ˆP=0.65/ME=0.30. ˆP=0.80/ME=0.15.

𝑃ˆ=0.80/𝑀𝐸=0.15.

In binomial methods, a statistics instructor at a local college sampled 100 of her students and found that 25 of them actually liked statistics. What is the 95% confidence interval for the population proportion of students liking statistics? n^p(1−^p) = 22.50 CI = (0.246, 0.254). CI = (0.165, 0.335). CI = (0.254, 0.246). CI = (0.213, 0.287).

CI = (0.165, 0.335).

In binomial methods, a mathematics instructor at a local college felt that more students actually like mathematics than the 25% of students who like statistics. To prove her case, she sampled 250 of her students and found that 25 of them actually liked mathematics. What is the 95% confidence interval for the population proportion of students liking mathematics? n^p(1−^p) = 22.50 CI = (0.063, 0.137). CI = (0.089, 0.111). CI = (0.081, 0.119). CI = (0.0996, 0.100).

CI = (0.063, 0.137).

In binomial methods, a study was done where 74 patients with ulcers were given a drug designed to treat ulcers. After six weeks, 42 of the patients reported a healing of their ulcer ˆP = 0.568. The FDA will approve a drug if more than 50% of the population will experience healing at a 95% level of confidence. Should the FDA approve this drug? (nˆp(1−ˆp)=18.16) Yes, because the population proportion could be as high as 68%. No, because the condition to use the normal approximation is not met. Yes, because the sample proportion is greater than 50%. No, because the population proportion could be as low as 46%.

No, because the population proportion could be as low as 46%.

In binomial methods, a recent study found that 37% of pet owners talked to their pet on the answering machine. This being hard to believe, a veterinarian surveyed 150 pet owners and found that 54 of them did talk to their pets on an answering machine. Analyze this situation with a hypothesis test at a 95% level of confidence to find out if less than 37% of people talk to their pet on an answering machine? (np(1−p)=35.0)? Yes, because ˆp=0.36. No, because p-value = 0.8062. No, because the p-value = 0.4013. Yes, because the test statistic z = -0.25 .

No, because the p-value = 0.4013.

In binomial methods, a study found that 85% of adult Americans ate a salad at least once per week. A local restaurant owner wondered if this was true for college students. She queried 225 college students and found that 175 students ate a salad at least once a week. Analyze this situation with a hypothesis test at a 95% level of confidence to find out if 85% is a proper proportion for college students? (np(1−p)=28.7)? No, because p-value = 0.0012. No, because the test statistic = -5.23. No, because the p-value = 0.0024. No, because the test statistic = -2.62.

No, because the p-value = 0.0024.

In binomial methods, a famous basketball player (Shaquille) was known to struggle with free throws making only 43.8% of them. His coach sent him to a free throw specialist who worked with him for five days. Then the&player shot 80 free throws and made 39 of them. Analyze this situation with a hypothesis test at a 95% level of confidence to find out if the free throw specialist was successful? (np(1−p)=)? All these other answers. No, because p-value = 0.1867. No, because the critical value z = 1.64. No, because the test statistic z = 0.89.

All these other answers.

In binomial methods, a May 1999 study found that 57.8% of households with internet by telephone dial-up watched TV during prime-time hours. A more recent study questioned 1,025 households with internet by cable and found that 575 households watched TV during prime-time hours. Analyze this situation with a hypothesis test at a 95% level of confidence to find out if the TV viewing behavior increased due to internet access by cable? (np(1−p)=250)? No, because p-value = 0.1357. No, because the critical value = 1.96. All of these other answers. No, because the test statistic = -2.23.

No, because p-value = 0.1357.

In binomial methods, what is the statistical method for relationship between two binomial variables actually measuring? If the linear relationship is mostly horizontal. If the two variables are correlated or not. If the two variables have a linear relationship. If the two variables are independent or not.

If the two variables are independent or not.

In binomial methods, can the Chi Square Test for Independence be used with continuous data values? No, it can only be used with categorical data values. Yes, as long as the continuous data is binned first. No, but it can be used with tweaked discrete data values. No, it can only be used with binomial data values.

No, it can only be used with binomial data values.

In binomial methods, what type of information does the Chi Square Test for Independence give? Reliable information. Sample information. Probability information. Population information.

Population information.

In binomial methods, does the Chi Square Test for Independence result in a p-value? Yes, as it is a hypothesis test. No, as it is a counting method and does not give p-values. Yes, as you can get probability from the Chi Square distribution. No, as it results in a range of reasonable values.

Yes, as it is a hypothesis test.

In binomial methods, what is the range / the shape, of almost all Chi-Square curves? (-∞, 0) / Skewed right. (0, ∞) / Symmetrical. (-∞, +∞) / Symmetrical. (0, ∞) / Skewed right.

(0, ∞) / Skewed right.

In binomial methods, the components of a 2x2 table are shown below. Which of these components are also part of a 2x2 contingency table for two binomial variables? A. Row Variable B. Column Variable C. Table Cells C. A and B. None of these other answers. A, B, and C.

A, B, and C.

In binomial methods, what method is used in this ebook to check that the assumptions of the Chi-Square test are met? np(1−p) is more than 10. Total count is more than 30. No observed frequency is more than 5. No expected frequency is less than 5.

No expected frequency is less than 5.

In binomial methods, after the observed frequencies are found for a contingency table, was other information is needed to calculate the expected frequencies? The researcher's belief of the true values. The totals for each row and column, and for the entire table. Which table, z or t, to use to get probability. n and p to calculate the mean and standard deviation.

The totals for each row and column, and for the entire table.

In binomial methods, what information is given by the expected frequencies? The cell frequencies as predicted by the normal curve. How far off are the observed frequencies were from true values. The cell frequency expected by the researcher. The cell frequency if the two variables are independent.

The cell frequency if the two variables are independent.

In binomial methods, how are the expected frequencies calculated? All these other answers. From Row Proportion x Column Proportion x Table Total. From the Row Total, Column Total and the Table Total. From (Row Total*Column Total)/Table Total

All these other answers.

In binomial methods, what fundamental concept of statistics is the Chi-Square test based upon? The location and spread of the observed frequencies. The balance of the observed frequencies in the contingency table. The deviation between the observed and expected frequencies (Oi − Ei). The relationship between the observed and expected frequencies.

The deviation between the observed and expected frequencies (Oi − Ei).

In binomial methods, the calculation of the chi-square test statistic is similar to what other calculation method already seen in this ebook? The summing calculation for average. The z-score calculation for correlation. The sum-of-squares calculation for variance. The minimum significant difference calculation for the Tukey table.

The sum-of-squares calculation for variance.

In binomial methods, what is the chi-square test of independence? A hypothesis test for three columns of categorical data. A hypothesis test for two columns of binomial data. A Shapiro-Wilk test for normality. A hypothesis test in two dimensions.

A hypothesis test for two columns of binomial data.

In binomial methods, which choice below is part of a chi-square test for independence? Sum the counts for each individual. Arrange in a 2x2 table and calculate the row, column, and table totals. Calculate the sample averages of individuals having the same set of data values. Write the set of hypotheses -H0:x2=0; H1:X2≠0.

Arrange in a 2x2 table and calculate the row, column, and table totals.

In binomial methods, in a chi-square test of independence, what is the statistical meaning of the null hypotheses? The two binomial variables are correlated with each other. The two binomial variables are independent of each other. The two binomial variables are significant from each other. The two binomial variables are dependent on each other.

The two binomial variables are independent of each other.

In binomial methods, in a chi-square test of independence, what type of hypothesis test situation is this? A middle body situation. A two-tail situation. A right-tail situation. A left-tail situation.

A right-tail situation.

In binomial methods, what is the difference between a 2x2 table of descriptive statistics and a 2x2 table used for the Chi-Square test for independence? The chi-square table includes observed frequencies. The chi-square table includes the deviation frequencies. The chi-square table is a 3x3 table. The chi-square table includes expected frequencies.

The chi-square table includes expected frequencies.

In binomial methods, in a chi-square test of independence, what is a p-value? The two tail areas from the test statistic to ±infinity. The right-tail area from the test statistic to positive infinity. The body area from the critical value to the test statistic. The tail area from the critical value to positive infinity.

The right-tail area from the test statistic to positive infinity.

In binomial methods, in the results of a chi-square test of independence shown below, are these two binomial variables independent, or dependent? Contingency table Tests: prob>chi square --> likelihood ratio --> 0.0005* Attending class and passing an exam are dependent, because the p-value = 0.005. Attending class and passing an exam are independent, because the chi-square test statistic = 11.988. Attending class and passing an exam are dependent, because the observed frequencies are close to the expected frequencies. Attending class and passing an exam independent, because the p-value = 0.005.

Attending class and passing an exam are dependent, because the p-value = 0.005.

In binomial methods, in the results of a chi-square test of independence shown below, are these two binomial variables independent, or dependent? Contingency table Tests: prob>chi square --> likelihood ratio --> 0.3155* These variables are dependent, because chi-square test statistic = 1.007. Attending class and passing an exam are dependent, because the null hypothesis was rejected. These variables are independent, because chi-square = 1.007 is bigger than the critical value = 0.999. Attending class and passing an exam are independent, because the p-value = 0.3155.

Attending class and passing an exam are independent, because the p-value = 0.3155.

In binomial methods, in the results of a chi-square test of independence shown below, are these two binomial variables unrelated, or related? Contingency table Tests: prob>chi square --> likelihood ratio --> 0.0323* Being overweight and eating fast food are not related, because RSquare = 0.0622. Being overweight and eating fast food are related, because the expected count in three of the cells are greater than 10. Being overweight and eating fast food are related, because the column totals are the same as the row totals. Being overweight and eating fast food are related, because the p-value = 0.0323.

Being overweight and eating fast food are related, because the p-value = 0.0323.