Hypothesis Testing and Statistical Inference

1. More than 200, 000 people worldwide take the GMAT examination each year as they apply for MBA programs. Their scores vary Normally with the mean about µ = 525 and standard deviation Ϭ = 100. One hundred students go through a rigorous training program designed to raise their GMAT scores. Suppose the average score for the 100 students is 541.4. At the .03 level of significance, has the training program worked.
a. Test the hypothesis using all three methods.
b. State the Type I and Type II errors.
c. As a student, which error do you believe is the most egregious?
d. As the B-School, which error do you believe is the most egregious?
e. Find β (530)
f. Find β (545)
g. What is the power of the test when µ = 545

2. The U.S. Energy Information Administration (US EIA) reported that the average price of regular gasoline is $2.76. The US EIA updates its estimates of average gas prices on a weekly basis. Assume the standard deviation is $.25 for the price of a gallon of regular gasoline and recommend the appropriate sample size for US EIA to use if they wish to report the margin of error to be $.10 at the 95% level of confidence.

3. According to statistics reported on CNBC, a surprising number of motor vehicles are not covered by insurance. Sample results consistent with the CNBC report, showed that 46 out of 200 vehicles were not covered by insurance.
a. Develop a 95% confidence interval for the population proportion.

b. State in words what this means.

4. A random sample of 16 airline passengers at the Atlanta Airport showed that the mean time spent waiting in line to check in at the ticket counter was 31 minutes with a standard deviation of 7 minutes. Construct a 99% confidence interval for the mean time spent waiting in line by all passengers at the airport.

5. Write the null and alternate hypotheses for each of the following examples. Determine if each is a case of a two-tailed, a left-tailed or a right-tailed test.
a. To test if the mean amount of time spent per week watching sports on television by all adult men is more than 9.5 hours.
b. To test if the mean amount of money spent by all customers at a supermarket is $105.
c. To test whether the mean starting salary of college graduates is lower than $59,000 per year.
d. To test if the mean waiting time at a drive through window at a fast-food restaurant during rush hour differs from 10 minutes.
e. To test if the mean hours spent per week studying statistics for all students is more than 3 hours.

6. Given the following null and alternative hypotheses.

Ho :  ≤ 1000

Ha :  > 1000

And x- bar = 980 s = 205 n = 100  = .06

a. Write the decision rule using the critical value approach.
b. Write the decision rule using the p-value approach.
c. Write the Type I and Type II Errors
d. What is the probability of making a Type I error
Note: The answers must be specific for this problem