Do the mean weights of male college freshmen and male college seniors differ? There are arguments for and against this question. The mean weight. Hx of college freshmen will be compared to the mean weight. Hy of college seniors. The true values of Hx and Hy are unknown. It is recognized that the true standard deviations are - 13 for male college freshmen and dy= 24 for male college seniors. We take a random sample of m= 431 college freshmen and a random sample of n=289 college seniors. The mean weights were x 178 for male college freshmen and y 185 for male college seniors. Assuming independence between the samples and assuming the weights are normally distributed we would like to estimate - Hy a) What is the standard deviation of the distribution of b) What is the standard deviation of the distribution of x-y?[ c) Create a 95% confidence interval for H- Hy? ( d) What is the length of the confidence interval in part c)? [ e) If we let n stay at 289 but vary m, what is the smallest m for which the length of the 95% confidence interval would be 5.8 or less? f) Copy your R script for the above into the text box here.
Do the mean weights of male college freshmen and male college seniors differ? There are arguments for and against this question. The mean weight. Hx of college freshmen will be compared to the mean weight. Hy of college seniors. The true values of Hx and Hy are unknown. It is recognized that the true standard deviations are - 13 for male college freshmen and dy= 24 for male college seniors. We take a random sample of m= 431 college freshmen and a random sample of n=289 college seniors. The mean weights were x 178 for male college freshmen and y 185 for male college seniors. Assuming independence between the samples and assuming the weights are normally distributed we would like to estimate - Hy a) What is the standard deviation of the distribution of b) What is the standard deviation of the distribution of x-y?[ c) Create a 95% confidence interval for H- Hy? ( d) What is the length of the confidence interval in part c)? [ e) If we let n stay at 289 but vary m, what is the smallest m for which the length of the 95% confidence interval would be 5.8 or less? f) Copy your R script for the above into the text box here.
Transcribed Image Text:Do the mean weights of male college freshmen and male college seniors differ? There are arguments for and against this question. The mean weight, μx of college freshmen will be compared to the mean weight, My of college seniors. The true values of Mx and My are unknown. It is recognized that the true standard deviations are x =
13 for male college freshmen and dy = 24 for male college seniors. We take a random sample of m = 431 college freshmen and a random sample of n=289 college seniors. The mean weights were x = 178 for male college freshmen and y = 185 for male college seniors. Assuming independence between the samples and assuming the
weights are normally distributed we would like to estimate My - My.
a) What is the standard deviation of the distribution of x?[
b) What is the standard deviation of the distribution of x-y?
c) Create a 95% confidence interval for Mx - Hy?
d) What is the length of the confidence interval in part c) ?
e) If we let n stay at 289 but vary m, what is the smallest m for which the length of the 95% confidence interval would be 5.8 or less?
f) Copy your R script for the above into the text box here.
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