# Testing Hypotheses and Confidence Intervals

A random sample of size 64 has sample mean 24 and sample standard deviation 4.

d. Is it appropriate to use the t distribution to compute a confidence interval for the population mean? Why or why not?

e. Construct a 95% confidence interval for the population mean.

f. Explain the meaning of the confidence interval you just constructed.

How much do adult male grizzly bears weigh in the wild? Six adult males were captured, tagged and released in California and here are their weights:

480, 580, 470, 510, 390, 550

g. What is the point estimate for the population mean?

h. Construct at 90% confidence interval for the population average weight of all adult male grizzly bears in the wild.

i. Interpret the confidence interval in the context of this problem.

After going to a fast food restaurant, customers are asked to take a survey. Out of a random sample of 340 customers, 290 said their experience was "satisfactory." Let p represent the proportion of all customers who would say their experience was "satisfactory."

j. What is the point estimate for p?

k. Construct a 99% confidence interval for p.

l. Give a brief interpretation of this interval.

Suppose the p-value for a right-tailed test is .0245.

a. What would be your conclusion at the .05 level of significance?

b. What would the p-value have been if it were a two-tailed test?

A random sample has 42 values. The sample mean is 9.5 and the sample standard deviation is 1.5. Use a level of significance of 0.02 to conduct a left-tailed test of the claim that the population mean is 10.0.

a. Are the requirements met to run a test like this?

b. What are the hypotheses for this test?

c. Compute the test statistic and the p-value for this test.

d. What is your conclusion at the 0.02 level of significance?

MTV states that 75% of all college students have seen at least one episode of their TV show "Jersey Shore". Last month, a random sample of 120 college students was selected and asked if they had seen at least one episode of the show. Out of the 120, 85 of them said they had seen at least one episode. Is there enough evidence to claim the population proportion of all college student that have watched at least one episode is less than 75% at the 0.05 level of significance?

a. Are the requirements met to run a test like this?

b. What are the hypotheses for this test?

c. Compute the test statistic and the p-value for this test.

d. What is your conclusion at the 0.05 level of significance?

#### Solution Summary

The solution gives detailed answers for a set of 4 questions on performing hypothesis testing, constructing confidence intervals and interpreting p-value.