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# General Statistics

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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.

##### 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.

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###### Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

##### Measures of Central Tendency

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