Chapter 9, question 5: please answer all

5. The 1 statistic, the t distribution, and sample size The average duration of labor from the rst contraction to the birth of the baby In women over 35 who have not previousiy 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 iabor 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 rst need to calculate the estimated standard error. The estimated standard error is SM: ' V . The t statistic is _._L . I New 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 i ."The new : t'statistic is ' . Note that the t 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 rst sample size on the slider, and click the radio button with the single orange line. Move the prange 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. What is the probability of getting the 1: statistic or something more extreme for the sample $29 of s n = 29? p = " . What is the probability of getting the t statistic or something more extreme for the sample size of n - 75? up -' ' . ' The t distribution Is ' with a smaller or. (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 Wages!)