5.1

There are two types of estimators of the population mean, the point estimator and the interval estimator. Please match each of the following estimators with their appropriate statistical method. A. Confidence Interval B. Sample Average

Point- B. Sample Average Interval.- A. Confidence Interval

Two common statistical estimators of the population mean are the sample average and the confidence interval. Which one of these statistics is more useful to give information about the value of a population mean? a)Confidence interval, as it is wider and has a greater chance of being correct. b)Sample average, as it is the best guessed value for the mean. c)Both, as they both estimate the same value (the population mean). d)Confidence interval, as it shows how far the mean might be from the average.

d)Confidence interval, as it shows how far the mean might be from the average.

Why is the confidence interval method the best method to get an interval estimate of the population mean? a)All of the other answers. b)It has a higher level of confidence than other interval estimators. c)It uses the most information from the distribution of the data values. d)It gives a wider estimate than the sample average.

c)It uses the most information from the distribution of the data values.

What is a major weakness in the method of a confidence interval? a)A confidence interval can give more than one interval for the population mean. b)Values outside of the confidence interval are not likely values for the population mean. c)Confidence intervals can be changed just by changing the level of confidence. d)A confidence interval does not give a degree of reasonableness for any value to be the population mean.

d)A confidence interval does not give a degree of reasonableness for any value to be the population mean.

The logic of a confidence interval comes from reversing the logic of the sampling distribution of the sample average. Thus, the schematic curve for a confidence interval is centered over which statistic for location? a)Population mode (Mode). b)Population mean (μ). c)Sample median (M). d)Sample average (¯x).

d)Sample average (¯x).

What is the name of the spread in a confidence interval? a)The coefficient of variation. b)The standard error. c)The standard deviation. d)The margin of error.

d)The margin of error.

Select two choices below that make up the two parts of a margin of error in a confidence interval? a)The level of predictiveness in the confidence interval method. b)The level of confidence in the confidence interval method. c)The standard error of the sample average. d)The standard deviation of the data values.

b)The level of confidence in the confidence interval method. c)The standard error of the sample average.

Please match each of the following changes in the calculation of the margin of error with their effect on the width of a confidence interval. Note which answer goes with which input change (n ,CL). A. Wider (CL). B. Narrower (CL). C. Narrower (n). D. Wider (n).

Increase sample size.- C. Narrower (n). Decrease sample size.- D. Wider (n). Increase level of confidence.- A. Wider (CL). Decrease level of confidence.- B. Narrower (CL).

The schematic curve for a confidence interval divides the curve into several regions. Which region will always contain the population mean? a)Significance region. b)Middle region. c)Mean region. d)Confidence region.

d)Confidence region.

The size of the confidence region is given by the size of the confidence level. What is a simple meaning of the confidence level? a)How many times out of 100 the method was calculated correctly. b)How confident to be that the confidence interval contains the value of the population mean. c)How many times out of 100 the method will give an incorrect answer. d)How many times out of 100 the method will give a correct answer.

d)How many times out of 100 the method will give a correct answer.

What points on the real number line separate the confidence region from the significance regions? a)The schematic values. b)The critical values. c)The confidence values. d)The significance values.

b)The critical values.

What is the size of the significance region? a)Alpha (α). b)Significance level (SL). c)Beta (β). d)Confidence level (CL).

a)Alpha (α).

Is it guaranteed that confidence interval method will give an interval containing the population mean every time? a)Yes, every confidence interval contains the population mean. b)No, probabilistic data almost never gives a correct answer. c)No, the method will give an incorrect interval alpha (α) percent of the time. d)No, the correctness of the method is limited by the quality of the data input.

c)No, the method will give an incorrect interval alpha (α) percent of the time.

Please match each of the following statistics with how often they give the true value of the population mean. A. Always never. B. CL percent of the time. C. Almost never.

Sample average.- C. Almost never. Confidence interval.- B. CL percent of the time. Sample standard deviation.- A. Always never.

Confidence intervals can be thought to be composed of two parts, a middle value and a spread value. Please match each of the following parts of a confidence interval with their appropriate statistics. A. The value of the sample average. B. The value of the margin of error.

Middle.- A. The value of the sample average. Spread- B. The value of the margin of error.

In a confidence interval, what information does the confidence level give? a)The proportion of times the confidence interval includes the population mean. b)The proportion of times the population mean is correct. c)The proportion of times the confidence interval should be trusted. d)The proportion of times the calculations are correct.

a)The proportion of times the confidence interval includes the population mean.

In the science of statistics, why is the method of confidence intervals needed to get information about the population mean? a)As intervals were known to be valuable in mathematics so the same concept was applied in statistics. b)As the population mean cannot be known exactly in this course. c)As the population mean cannot be determined exactly from probabilistic sample data values. d)As a single value was not considered valid enough for the population mean.

c)As the population mean cannot be determined exactly from probabilistic sample data values.

The statistical logic for a confidence interval is based on reversing already known logic for another statistic. What is this other logic? a)The logic for the sampling distribution of the sample average. b)The logic for the distribution of the population mean. c)The logic for the level of confidence. d)The logic for the distribution of the data.

a)The logic for the sampling distribution of the sample average.

Is the interval shown below properly denotated for a confidence interval? (115,97) a)Yes, as this interval has a middle part and a spread part. b)No, as the value of the sample average must be in the middle of the interval. c)No, values in the parentheses must go from lowest to highest. d)Yes, this is a proper denotation for a confidence interval.

c)No, values in the parentheses must go from lowest to highest.

Looking in a schematic curve from the point of view of probability, what type of situation is a confidence interval? a)A right (or left) tail area. b)A middle body area. c)A right (or left) body area. d)A side area.

b)A middle body area.

The curve in a schematic curve can be centered over different values to give different information about the data values. Please match each value below with what information is given about the data values. A. A range of likely values for the sample average. B. A range of likely values for the population mean.

The population mean.- A. A range of likely values for the sample average. The sample average.- B. A range of likely values for the population mean.

The lower and upper confidence limits for a confidence interval can be seen in a schematic curve. The two confidence limits are just the x-values of a middle body area in a schematic curve. a)Never true. b)None of the other answers. c)Sometimes true. d)True.

d)True.

What is the main strength of a confidence interval? a)Gives a level of confidence for the value of the population mean. b)It is easy to calculate and to interpret its meaning. c)Gives a range of unlikely values for the population mean. d)Gives a range of likely values for the population mean.

d)Gives a range of likely values for the population mean.

What is the major weakness of a confidence interval? a)Some confidence intervals give practically impossible values. b)Every value inside the interval is equally likely to be the population mean. c)Some confidence intervals are too wide to be useful. d)Confidence intervals do not explicitly give the middle and the spread values.

b)Every value inside the interval is equally likely to be the population mean.

What is the correct equation for a confidence interval with t-values? Choose from the following options. a)CI%=¯x±t(α/2,n−1)(s/√n) b)CI%=μ±t(α/2,n−1)(s/√n) c)CI%=¯x±t(α/2,n−1)(√s/n) d)CI%=¯x±t(α/2,n−1)(s/n)

a)CI%=¯x±t(α/2,n−1)(s/√n)

Consider the size of the significance region, what is its appropriate symbol and how is it calculated? a)α=1+CL. b)α=1−CL. c)β=CL−1. d)σ=CL−α.

b)α=1−CL.

Will every confidence interval contain the value of the population mean? a)No, but it will most of the time. b)No, only the confidence level proportion of the time. c)Yes, unless the calculations are done incorrectly. d)No, as the population mean is either inside or outside the confidence interval.

b)No, only the confidence level proportion of the time.

What is the critical value for a 95% confidence interval with 22 data values and the sample standard deviation? a)Critical value = 1.960. b)Critical value = 1.721. c)Critical value = 2.080. d)Critical value = 2.074.

c)Critical value = 2.080.

What is the critical value for a 90% confidence interval with 31 data values and the sample standard deviation? a)Critical value = 1.697. b)Critical value = 1.640. c)Critical value = 1.696. d)Critical value = 1.310.

a)Critical value = 1.697.

What is the critical value for a 99% confidence interval with 10 data values and the sample standard deviation? a)Critical value = 3.169. b)Critical value = 3.250. c)Critical value = 2.821. d)Critical value = 2.764.

b)Critical value = 3.250.

In the confidence interval equation shown below, what part of the equation is the margin of error? CI%=¯x±t(α/2,n−1)(s/√n) a)ME=¯x±(s/√n) b)ME=(s/√n) c)ME=t(α/2,n−1)(s/√n) d)ME=t(α/2,n−1)

c)ME=t(α/2,n−1)(s/√n)

If the degrees of freedom gives the number of units of information, what does the margin of error give? a)Half the width of a confidence interval. b)The entire width of a confidence interval. c)Half the size of the significance region. d)The level of confidence in the confidence interval.

a)Half the width of a confidence interval.

When the confidence level is increased, how does the width of the confidence interval change? a)Widens, as the middle body area gets larger. b)Narrows, as there is more information in the confidence interval. c)Narrows, as there is more confidence in the method. d)Widens, as the tail areas get larger.

a)Widens, as the middle body area gets larger.

When the number of data values is increased, how does the width of the confidence interval change? a)Narrows, as the degrees of freedom get larger. b)Widens, as more data values mean more information. c)Narrows, as the standard error of the sample average gets smaller. d)Widens, as the calculations increase in size.

c)Narrows, as the standard error of the sample average gets smaller.