Suppose X is a random variable with normal distribution and Var(X)=100. Suppose we have a sample of X. The sample size is 100 and sample mean is 10. When giving a 90% confidence interval of μ. What is the significant level.

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…

The time it takes students to finish the Statistics Exam is known to be normally distributed with a standard deviation of σ=25 minutes. An instructor wants to estimate the mean exam time with an 80% confidence interval. What size sample should she use to estimate the mean exam time to within 5 minutes?

The heights of 9 men were taken with sample mean of 165 cm and standard deviation 5 cm. The heights of 7 Japanese women were taken with sample mean of 150 cm and standard deviation 3 cm. Assuming that the population standard deviations for heights of men and women are both the same, construct the 95% confidence interval for the difference in mean heights between men and women.

Can you solve this problem about the confidence interval?

The president of a large university wishes to compare the standard deviation of the ages of students presently enrolled to previous years. The distribution of ages has been approximately normal. Find the 90% confidence interval for the population standard deviation of the student ages of the University. A random sample of 20 university students has a standard deviation of 6.1 years in a mean of 23.8 years what is the confidence interval of the population standard deviation?

A certain counselor wants to compare mean IQ scores for two different social groups. A random sample of 15 IQ scores from group 1 showed a mean of 117 and a standard deviation of 17 , while an independently chosen random sample of 9 IQ scores from group 2 showed a mean of 112 and a standard deviation of 15 . Assuming that the populations of IQ scores are normally distributed for each of the groups and that the variances of these populations are equal, construct a 90% confidence intervalfor the difference −μ1μ2 between the mean μ1 of IQ scores of group 1 and the mean μ2 of IQ scores of group 2 . Then find the lower limit and upper limit of the 90% confidence interval. Carry your intermediate computations to at least three decimal places. Round your responses to at least two decimal places. (If necessary, consult a list of formulas.)