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The average duration of labor from the first contraction to the birth of the baby in women over 35 who have not previously given birth and who did not use any pharmaceuticals is 16 hours. Suppose you have a sample of 29 women over 35 who have not previously given birth who exercise daily, and who have an average duration of labor of 17.3 hours and a sample variance of 37.2 hours. You want to test the hypothesis that women over 35 who have not previously given birth and who exercise daily have a different duration of labor than all women over 35 who have not previously given birth. Calculate the t statistic. To do this, you first need to calculate the estimated standard error. The estimated standard error is sM= The t statistic is Now suppose you have a larger sample size n = 75. Calculate the estimated standard error and the t statistic for this sample with the same sample average and the same standard deviation as above, but with the larger sample size. The new estimated standard error is v . The newt statistic is Note that thet statistic becomes as n becomes larger. Use the Distributions tool to look at the t distributions for different sample sizes. To do this, choose the Degrees of Freedom for the first sample size on the slider, and click the radio button with the single orange line. Move the orange vertical line to the right until the number below the orange line is located on the t statistic. The probability of getting that t statistic or one more extreme will appear in the bubble with the orange type. Now repeat the process for the other sample.

The average duration of labor from the first contraction to the birth of the baby in women over 35 who have not previously given birth and who did not use any pharmaceuticals is 16 hours. Suppose you have a sample of 29 women over 35 who have not previously given birth who exercise daily, and who have an average duration of labor of 17.3 hours and a sample variance of 37.2 hours. You want to test the hypothesis that women over 35 who have not previously given birth and who exercise daily have a different duration of labor than all women over 35 who have not previously given birth. Calculate the t statistic. To do this, you first need to calculate the estimated standard error. The estimated standard error is sM= The t statistic is Now suppose you have a larger sample size n = 75. Calculate the estimated standard error and the t statistic for this sample with the same sample average and the same standard deviation as above, but with the larger sample size. The new estimated standard error is v . The newt statistic is Note that thet statistic becomes as n becomes larger. Use the Distributions tool to look at the t distributions for different sample sizes. To do this, choose the Degrees of Freedom for the first sample size on the slider, and click the radio button with the single orange line. Move the orange vertical line to the right until the number below the orange line is located on the t statistic. The probability of getting that t statistic or one more extreme will appear in the bubble with the orange type. Now repeat the process for the other sample.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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4. The t statistic, the t distribution, and sample size

**Understanding Labor Duration Studies in Women Over 35** The average duration of labor from the first contraction to the birth of the baby in women over 35, who have not previously given birth and who did not use any pharmaceuticals, is 16 hours. Suppose you have a sample of 29 women over 35 who have not previously given birth, who exercise daily, and who have an average duration of labor of 17.3 hours with a sample variance of 37.2 hours. You want to test the hypothesis that women over 35 who have not previously given birth and who exercise daily have a different duration of labor than all women over 35 who have not previously given birth. **Calculate the t Statistic** To calculate the t statistic, you first need to determine the estimated standard error: - The estimated standard error is SM = _______ . - The t statistic is _______ . Now suppose you have a larger sample size (n = 75). Recalculate the estimated standard error and the t statistic for this sample with the same sample average and the same standard deviation as above, but with the larger sample size: - The new estimated standard error is _______ . - The new t statistic is _______ . **Notes on t Statistics** Notice how the t statistic changes as n becomes larger. **Using the Distributions Tool** To explore t distributions for various sample sizes, use the Distributions tool: - Choose the Degrees of Freedom for the first sample size on the slider. - Click the radio button with the single orange line. - Move the orange vertical line to the right until the number below the orange line is aligned with the t statistic. The probability of obtaining that t statistic or a more extreme value will appear in the bubble with the orange type. - Repeat the process for the other sample.
Transcribed Image Text:**Understanding Labor Duration Studies in Women Over 35** The average duration of labor from the first contraction to the birth of the baby in women over 35, who have not previously given birth and who did not use any pharmaceuticals, is 16 hours. Suppose you have a sample of 29 women over 35 who have not previously given birth, who exercise daily, and who have an average duration of labor of 17.3 hours with a sample variance of 37.2 hours. You want to test the hypothesis that women over 35 who have not previously given birth and who exercise daily have a different duration of labor than all women over 35 who have not previously given birth. **Calculate the t Statistic** To calculate the t statistic, you first need to determine the estimated standard error: - The estimated standard error is SM = _______ . - The t statistic is _______ . Now suppose you have a larger sample size (n = 75). Recalculate the estimated standard error and the t statistic for this sample with the same sample average and the same standard deviation as above, but with the larger sample size: - The new estimated standard error is _______ . - The new t statistic is _______ . **Notes on t Statistics** Notice how the t statistic changes as n becomes larger. **Using the Distributions Tool** To explore t distributions for various sample sizes, use the Distributions tool: - Choose the Degrees of Freedom for the first sample size on the slider. - Click the radio button with the single orange line. - Move the orange vertical line to the right until the number below the orange line is aligned with the t statistic. The probability of obtaining that t statistic or a more extreme value will appear in the bubble with the orange type. - Repeat the process for the other sample.
The diagram illustrates a t-distribution graph, where the x-axis ranges from -3.0 to 3.0. The graph displays a symmetrical, bell-shaped curve highlighted in blue, representing the probability density function of a t-distribution. To the left of the graph, there is a control panel labeled "t Distribution," showing the "Degrees of Freedom = 52" with a slider bar below that can be adjusted. Below the slider are two radio buttons, the first selected, displaying an icon of a curve with vertical lines, and the second grayed-out, without lines. Under the graph, the text provides a comparison task for two sample sizes: - What is the probability of getting the t statistic or something more extreme for the sample size of n = 29? p = ______▼. - What is the probability of getting the t statistic or something more extreme for the sample size of n = 75? p = ______▼. The task ends with a fill-in-the-blank exercise and a hint: "The t distribution is ________________________ ▼ with a smaller n. (Hint: To best see this, click the radio button in the tool with no vertical lines. Slowly move the Degrees of Freedom slider from the smallest value to the largest value, and observe how the shape of the distribution changes.)" This interactive tool illustrates how degrees of freedom and sample size affect the shape and probabilities within a t-distribution.
Transcribed Image Text:The diagram illustrates a t-distribution graph, where the x-axis ranges from -3.0 to 3.0. The graph displays a symmetrical, bell-shaped curve highlighted in blue, representing the probability density function of a t-distribution. To the left of the graph, there is a control panel labeled "t Distribution," showing the "Degrees of Freedom = 52" with a slider bar below that can be adjusted. Below the slider are two radio buttons, the first selected, displaying an icon of a curve with vertical lines, and the second grayed-out, without lines. Under the graph, the text provides a comparison task for two sample sizes: - What is the probability of getting the t statistic or something more extreme for the sample size of n = 29? p = ______▼. - What is the probability of getting the t statistic or something more extreme for the sample size of n = 75? p = ______▼. The task ends with a fill-in-the-blank exercise and a hint: "The t distribution is ________________________ ▼ with a smaller n. (Hint: To best see this, click the radio button in the tool with no vertical lines. Slowly move the Degrees of Freedom slider from the smallest value to the largest value, and observe how the shape of the distribution changes.)" This interactive tool illustrates how degrees of freedom and sample size affect the shape and probabilities within a t-distribution.
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