Hypothesis Testing-

Use the following 5 step method for all problems.

(i) State the hypotheses H0, H1, and identify the claim (notation is important, use population parameters)

(ii) Find the critical value(s) from the appropriate distribution, check conditions to determine the appropriate distribution

(iii) Compute the test value using the appropriate formula

(iv) Make a decision to reject or not reject the null hypothesis by comparing the test value to the critical value.

(v) Summarize the results in the context of the problem.

1.  A manufacturer states that the average lifetime of its light bulbs is 3 years.  The standard deviation is σ = 8 months.  A sample of fifty bulbs is taken and the average lifetime is found to be 34 months.

(a) Should the claim be rejected at the α = .05?

(b) Should the claim be rejected at the α = .10?

2. A travel agency says that it books an average of 42 people per trip to Atlantic City.  A sample of 10 trips showed a mean of 48 people booked and a sample standard deviation of s = 8.  At α = .01, test the claim.

3. Experts claim that 10% of murders are committed by women.  Is there enough evidence at α = .05 to reject the claim if in a sample of 67 murders, 10 were committed by women?

4. A bank manager claims that the average loan to the bank's customers is $4800.  The population standard deviation is $800.  A sample of 25 customers had an average loan of $4235.  At α = .10, does the evidence support the manager's claim?

5. How long does it take juniors to complete a standardized exam? The long-term average is 2.8 hours. We may assume that x has a normal distribution with σ = 0.8. A random sample of 12 juniors gave a sample mean of 2.2 hours. Does this indicate that the population mean time is different from 2.8 Hours? Use 5% level of significance.

6. A manufacturer claims that the standard deviation of the drying time of a certain type of paint is 18 minutes. A sample of five test panels produced a standard deviation of 21 minutes. Test the claim at α = .05.