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StatisticsQ&A LibraryResearchers compared cortisol levels of two samples of women at childbirth. The first group (n=48) underwent emergency cesarean section following induced labor and had a mean cortisol level of 445 with a standard deviation of 60. The second group (n=50) delivered either by cesarean section or vaginally following spontaneous labor, and had a mean cortisol level of 650 with a standard deviation of 75. Construct a two-sided 95% confidence interval for the difference between the two means. Assume equal variances. Give an interpretation of the confidence interval. You MUST show your work to receive full credit. Partial credit is available.Question

Asked Oct 29, 2019

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Researchers compared cortisol levels of two samples of women at childbirth. The first group (n=48) underwent emergency cesarean section following induced labor and had a mean cortisol level of 445 with a standard deviation of 60. The second group (n=50) delivered either by cesarean section or vaginally following spontaneous labor, and had a mean cortisol level of 650 with a standard deviation of 75. Construct a two-sided **95% confidence interval** for the difference between the two means. Assume equal variances. **Give an interpretation of the confidence interval**. You MUST show your work to receive full credit. Partial credit is available.

Step 1

** **

**Solution:**

**The critical value is obtained below:**

From the given information, the first group sample size n_{1} is 48, standard deviation s_{1} is 60 and mean is 445. The second group sample size n_{2} is 50, standard deviation s_{1} is 75 and mean is 650. The confidence level is 95%.

The level of significance=1-0.95=0.05.

The degrees of freedom= n_{1}+n_{2}–2=48+50-2=96

The critical value is,

From the EXCEL, using the formula, =T.INV.2T(0.05,5), the critical value is 1.985.

Step 2

**The two-sided 95% confidence interval for the difference between the two means is constructed below:**

The required 95%confidence interval is,

Step 3

**The confidence interval is interpreted below:**

There is 95% confident that difference between the two means lies between **&nda...**

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