The following random sample was selected from a normaldistribution: 4, 6, 3, 5, 9, 3.
a. Construct a 90% confidence interval for the populationmean.
b. Construct a 95% confidence interval for the populationmean.
c. Construct a 99% confidence interval for the populationmean.
d. Assume that the sample mean x and sample standard deviation sremain exactly the same as those you just calculated but are basedon a sample of n = 25 observations rather than n = 6 observations.Repeat parts a–c. What is the effect of increasing the sample sizeon the width of the confidence intervals?
e. Use Rejection region to test the null hypothesis that themean of the population is 6 against the alternative hypothesis,?<6. Use ? = .05.
f. Use p-Value to test the null hypothesis that the mean of thepopulation is 6 against the alternative hypothesis, ? ≠6. Use ? =.05.
