# General Statistics

T F 1. If the null hypothesis is stated that the average number of milligrams of sodium in a manufacturer's can of soup is 200 mg, an appropriate alternative hypothesis is that the average number of milligrams of sodium exceeds 200 mg.

T F 2. If a null hypothesis is tested and rejected at the a = 0.05 level, the same null hypothesis would also have been rejected had it been tested at the a = 0.01 level.

T F 3. If a calculated p value is relatively large, the implication is that the data are inconsistent with the null hypothesis such that it is likely that H0 should be rejected.

T F 4. If the null hypothesis is actually true and your decision has been to reject it, you have committed a Type I error.

1. A study was recently conducted that yielded a p value of 0.001 after all the data were analyzed. The researchers are correct to conclude that the data are

a. highly consistent with the null hypothesis.

b. insufficient to draw a conclusion and that more data need to be collected.

c. highly inconsistent with the alternative hypothesis.

d. indicative of a strong rejection of the null hypothesis.

2. Whenever a lower-tail test of the mean is being conducted, the critical region under the normal curve is the area under the curve that is located

a. to the right of -Zcutoff.

b. to the left of -Zcutoff.

c. between 0 and -Zcutoff.

d. between -Zcutoff and +Zcutoff.

The price-to-book value is a commonly used measure of whether a stock is over-priced or under-priced. The average price-to-book value for all gas utility stocks averaged 180% in 1998 and the standard deviation was 45%. A random selection of 36 gas utility stocks in August, 1999 yielded a mean of 195%.

a. Set up the null and alternative hypotheses to test if the average price-to-book value of the August, 1999 selection is greater than the 1998 national average for gas utility stocks.

b. Test your hypothesis using a = 0.05.

c. Find the p value.

d. What is your conclusion?

#### Solution Summary

T F 1. If the null hypothesis is stated that the average number of milligrams of sodium in a manufacturer's can of soup is 200 mg, an appropriate alternative hypothesis is that the average number of milligrams of sodium exceeds 200 mg.

T F 2. If a null hypothesis is tested and rejected at the a = 0.05 level, the same null hypothesis would also have been rejected had it been tested at the a = 0.01 level.

T F 3. If a calculated p value is relatively large, the implication is that the data are inconsistent with the null hypothesis such that it is likely that H0 should be rejected.

T F 4. If the null hypothesis is actually true and your decision has been to reject it, you have committed a Type I error.

1. A study was recently conducted that yielded a p value of 0.001 after all the data were analyzed. The researchers are correct to conclude that the data are

a. highly consistent with the null hypothesis.

b. insufficient to draw a conclusion and that more data need to be collected.

c. highly inconsistent with the alternative hypothesis.

d. indicative of a strong rejection of the null hypothesis.

2. Whenever a lower-tail test of the mean is being conducted, the critical region under the normal curve is the area under the curve that is located

a. to the right of -Zcutoff.

b. to the left of -Zcutoff.

c. between 0 and -Zcutoff.

d. between -Zcutoff and +Zcutoff.

The price-to-book value is a commonly used measure of whether a stock is over-priced or under-priced. The average price-to-book value for all gas utility stocks averaged 180% in 1998 and the standard deviation was 45%. A random selection of 36 gas utility stocks in August, 1999 yielded a mean of 195%.

a. Set up the null and alternative hypotheses to test if the average price-to-book value of the August, 1999 selection is greater than the 1998 national average for gas utility stocks.

b. Test your hypothesis using a = 0.05.

c. Find the p value.

d. What is your conclusion?