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Information about the population.
A column of population data values has more data values than a column of sample data values.
To get information about population data values.
Because the population mean was one of the first statistical methods developed.
Most of the data values are clustered close to the value of the mean.
All these other choices.
It best estimates the value of the population mean from the sample data values.
Estimate the population mean. - Confidence Intervals Test for the population mean. - Hypothesis Testing
An interval estimate of the population mean.
A conclusion to a statistical test about a population mean.
Step A: - Abstract problem information. Step 1: - Theorize probability information. Step 2: - Analyze sample information. Step 3: - Infer population information.
Get descriptive statistics. Write the two hypotheses.
The Schematic z-Curve. The z-Table.
Choose the appropriate equation.
Statistical information about the value of a population mean.
Because each data value brings a bit more information about the population data values.
Descriptive statistics, because they describe the data values in a column of sample data values.
Summarize the question text into a reasonable size.
μ (Population Mean): 0.5 σ, s (Standard Deviation): n/a n (Sample Size): 25 x̄ (Sample Mean): 0.55
μ (Population Mean): 1.2 σ (Population Standard Deviation): 0.01 n (Sample Size): 37 x̄ (Sample Mean): 1.15 s (Sample Standard Deviation): n/a
μ (Population Mean): 215,816 σ (Population Standard Deviation): 21,500 n (Sample Size): 58 x̄ (Sample Mean): 235,000 s (Sample Standard Deviation): 23,500
μ, σ (Population Mean/Standard Deviation): n/a n (Sample Size): 3,412 x̄ (Sample Mean): 1.7 s (Sample Standard Deviation): 0.7
That all Americans spend 4.5 hours.
Alpha (α).
μ : (23) σ : (3.7) n, x̅, s : (n/a)
μ : 14 n, σ, s : n/a x̄ : 12
μ : 4.1 σ : 0.7 n : 14 x̅ : 5.3 s : 1.2
μ, σ : n/a n1 : 30 n2 : 25 x̄1 : 78% x̄2 : 83% s1 : 10% s2 : 13%
μ : 17 σ : 10.5 n, x̄, s : n/a
The z-Table. This z-Equation: z = (x̅ - μ) / (σ / √n)
Step 1. : Draw the schematic. Step 2. : Calibrate the x-Axis. Step 3. : Load the problem. Step 4. : Solve for the answer.
The calculations for the method are chosen and performed.
Determining a population value from a sample values.
Abstract : n/a Theorize : A z-score from probability Analyze : A z-score from the sample Infer : n/a
Point: Sample Average Interval: Confidence Interval
Confidence interval, as it shows how far the mean might be from the average.
It uses the most information from the distribution of the data values.
A confidence interval does not give a degree of reasonableness for any value to be the population mean.
Sample average (¯x).
The margin of error.
The level of confidence in the confidence interval method. The standard error of the sample average.
Increase sample size: Narrower (n). Decrease sample size: Wider (n). Increase level of confidence: Wider (CL). Decrease level of confidence: Narrower (CL).
Confidence region.
How many times out of 100 the method will give a correct answer.
The critical values.
Alpha (α).
No, the method will give an incorrect interval alpha (α) percent of the time.
Sample average. : Almost never. Confidence interval. : CL percent of the time. Sample standard deviation. : Always never.
Middle: The value of the sample average. Spread: The value of the margin of error.
The proportion of times the confidence interval includes the population mean.
As the population mean cannot be determined exactly from probabilistic sample data values.
The logic for the sampling distribution of the sample average.
No, values in the parentheses must go from lowest to highest.
A middle body area.
The population mean: A range of likely values for the sample average. The sample average: A range of likely values for the population mean.
True.
Gives a range of likely values for the population mean.
Every value inside the interval is equally likely to be the population mean.
α = 1−CL.
No, only the confidence level proportion of the time.
Critical value = 2.080.
Critical value = 1.697.
Critical value = 3.250.
ME = t(α/2,n−1) (s/√n)
Half the width of a confidence interval.
Widens, as the middle body area gets larger.
Narrows, as the standard error of the sample average gets smaller.
Sample standard deviation / Degrees of freedom.
Values = 107 / 11.
No, as it is used to find the value of the population mean.
No, as finding the value of the population mean is the goal.
Any of these values could be a likely value for the population mean.
Not well, as 85 is higher than the upper confidence limit.
Yes, as CI = (76.3, 83.7).
Yes, as 87 is inside of CI = (81.989, 88.011)
No, as the two confidence intervals, (121.1, 128.9) and (133.4, 138.6) do not overlap.
Values = $11,000 / $1,276.
No, as the confidence interval for age = (30.64, 37.86).
CI = (67.0, 68.9).
Yes, as 66 inches is inside the confidence interval.
No, as all values inside the confidence interval are equally likely.
CI = (1.35, 5.85)
All of these other answers.
Grams = 0.6813 / 1.1494
CI = (14.97, 17.02).
- To learn the reasonableness that the null value is the value of the population mean. - To answer if the null value is less than, or greater than, the population mean.
How reasonable is the null value the value of the population mean.
Could the value of the population mean be less than, or greater than, the value in the null hypothesis.
- The individuals were randomly selected. - The sample average is normally distributed.
A: Abstract. : Relevant info from problem. 1: Theorize. : Probability info from theory. 2: Analyze. : Sample info from problem. 3: Infer. : Population info as a result.
Statistic = 𝑡0.
The currently believed value of the population mean.
The researcher's believed value of the population mean.
Acceptance Region. : A middle body area. Less than Rejection Region. : A left-tail area. Greater than Rejection Region. : A right-tail area. Not-Equal-To Rejection Region. : A two-tail area.
The critical value / From the z,t-Table.
From the t-equation (𝑡0=𝑥¯−𝜇/𝑠/√n).