4.the t-statistics,the t distribution,and sample size Complete: cnapter 9 Proble

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4.the t-statistics,the t distribution,and sample size

Complete: cnapter 9 Problem Set Due on Dec 8 at 11 PM EST 4. The t statistic, the t distribution, and sample size AaAa 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 SH-1.1326 The t statistic is 1.15 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 0.7043 The new t statistic is 1.85 Note that the t statistic becomes larger 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 il appear in the bubble with the orange type. Now repeat the process for the other sample. t Distribution Degrees of Freedom-52 3.0 -2.0 1.0 D.0 1.0 2.0 3.0 What is the probability of getting the t statistic or something more extreme for the sample size of n = 29? p = 0.1299 | . What is the probability of getting the t statistic or something more extreme for the sample size of n = 0.1299 .0342 0.0342 0.0145 0.2689 ution is flatter and more spread out 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.

Explanation / Answer

Solution:

(a) Since we have to given t statistics = 1.15 and n=29 , so we calculate p-value using the Excel function TDIST() as follows:

p-value = 0.1299 , Since used [TDIST(1.15,28,1)]

(b) Similarly we have to given t statistics = 1.85 and n=75,so we calculate p-value using the Excel function TDIST() as follows:

p-value = 0.0342 , Using ( TDIST(1.85,74,1) )

Cheers!!

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