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MATH Statistics

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A student union wants to obtain a 90% confidence interval for the proportion of “full time” students who hold a part-time job for 20 hours or more per week. For this purpose, they want to interview a sample of full-time students. They want a margin of error to be at most 0.1, i.e., the length of the confidence interval should not exceed 0.2. What is the minimum number of full-time students they should interview?
• A researcher wants to determine the difference between the gestational period (period of pregnancy) for two groups of women, namely, those who had normal pregnancies (group A) and those who suffered from a certain complication during pregnancy known as preeclampsia (group B). The following data shows the gestational periods (in weeks) for a sample of 14 women from group A and of 13 women from group B.
Gestational periods for sample from group A: 40, 41, 38, 40, 40, 39, 39, 41, 41, 40, 40, 40, 39, 38
Gestational periods for sample from group B: 38, 30, 32, 42, 30, 38, 35, 32, 38, 39, 29, 29, 32
Find a 95% confidence interval for the difference between the gestational periods of group A and group B, i.e., group A mean minus group B mean. Assume that the variances of the two groups are equal. State any other assumptions you make

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