A. What Are the Appropriate Null and Alternative Hypotheses?

BA 275 Quizzes

Winter 2007

Quiz #3

Name (please print)
Section (circle one) / 12noon – 1:50pm / 2:00 – 3:50pm / 4:00 – 5:50pm

Question 1. The mean area m of several thousand apartments in a new development is advertised to be 1250 square feet. A tenant group thinks that the apartments are smaller than advertised. They hire an engineer to measure a sample of apartments (n = 36) to test their suspicion.

A. What are the appropriate null and alternative hypotheses?

Null Hypothesis (H0) / m = 1250
Alternative Hypothesis (Ha) / m < 1250

B. If the sample mean is 1200 square feet, what is the conclusion of the test? Assume that population standard deviation s = 200 and a = 5%.

Statistical Conclusion (circle one) / Reject H0 / Do not reject H0
Support your statistical conclusion by providing a p-value of the test
OR
define the rejection region and calculate the test statistic / p-value = P( < 1200 )
= P( ) = 0.0668.
OR
Rejection region: Reject H0 if z < –1.645
Is the tenant group’s suspicion supported by the sample? (circle one) / Supported / Not supported

Question 2. Is the mean height for all adult American males between the ages of 18 and 21 now over 6 feet? If the population of all adult American males between the ages of 18 and 21 has mean height of m feet and standard deviation s feet, what are the appropriate null and alternative hypotheses?

a. H0: m = 6 vs. Ha: m > 6

b. H0: m = 6 vs. Ha: m < 6

c. H0: m = 6 vs. Ha: m ≠ 6

d. Not enough information to state H0 and Ha.

Answer / A. “Is the mean OVER 6 feet” is what we want to test. Thus, Ha: m > 6.

Question 3. The nicotine content in cigarettes of a certain brand is normally distributed, with mean (in milligrams) m and standard deviation s = 0.1. The brand advertises that the mean nicotine content of its cigarettes is 1.5, but measurements on a random sample of 100 cigarettes of this brand give a mean of 1.53. Is this evidence that the mean nicotine content is actually higher than advertised?

A. What are the appropriate null and alternative hypotheses?

Null Hypothesis (H0) / m = 1.5
Alternative Hypothesis (Ha) / m > 1.5

B. Given a = 5%, what are the statistical conclusion and the implication?

Statistical Conclusion (circle one) / Reject H0 / Do not reject H0
Support your statistical conclusion by providing a p-value of the test
OR
define the rejection region and calculate the test statistic / p-value = P( < 1.53 )
= P( ) = 0.0013.
OR
Rejection region: Reject H0 if z > +1.645
Is the mean nicotine content higher than advertised? (circle one) / Yes / No

Hsieh, P-H