Discuss the following:
Q1. In random samples of 25 from each of two normal populations, we found the following statistics:
x1 bar = 524 s1 = 129
x2 bar = 469 s2 = 131
a) estimate the difference between the two population means with 95% confidence.
b) repeat part a) increasing the standard deviations of s 1 to 255 and s 2 to 260.
c) describe what happens when the sample standard deviations get larger.
d) repeat part a) with samples of size 100.
e) discuss the effects of increasing the sample size.
Q2. Calculate the following:
a) Determine the sample size necessary to estimate a population mean to within 1 with a 90% confidence given that the population standard deviation is 10.
b) Suppose that the sample was calculated at 150. Estimate the population mean with 90% confidence.
Q3. a) Calculate the probability of a type ii error for the following hypotheses when u = 37:
ho: u = 40
h1: u < 40
the significance level is 5%, the population standard deviation is 5, and the sample size is 25.
b) repeat part (a) with a significance level = 15%.
c) What is the effect of increasing the significant level on the type ii error.