Question

Assume that a hypothesis test of the given claim will be conducted. Use  for a claim about a mean and  for a claim about a proportion.

a. Express the claim in symbolic form.

b. Identify the null hypothesis Ho.

c. Identify the alternative hypothesis HA.

d. Identify the test as being two-tailed, left-tailed, or right-tailed.

e. Identify the type I error for this test.

f. Identify the type II error for this test.

g. Assume that the conclusion is to reject the null hypothesis. State the conclusion in non-technical terms; be sure to address the original claim.

Assume that the conclusion is failure to reject the null hypothesis. State the conclusion in non-technical terms; be sure to address the original claim.

A. Department of Health claims that a pharmaceutical company makes cold capsules that contain amounts of acetaminophen with a mean different from the 500 mg amount indicated on the label.

B. The Laban Party standard bearer claims that he is currently favored by more than one-half of his constituency.

C. The Department of Education claims that over 2% of all adults are enrolled in school full-time.

D. The Land Transportation Office would like to know if motorists are being seduced by ads to buy higher octane gas than is useful. Test the claim that fewer than 10% of cars on the road have a design that benefits from higher octane gasoline.

Answer 1

A.

a.

The claim is that mean amount of acetaminophen is different than 500 mg

b.

The null hypothesis is that mean amount of acetaminophen in cold capsules is equal to 500 mg

c.

The alternate hypothesis is that mean amount of acetaminophen in cold capsules is different than 500 mg

d.

The test is two tailed, since we want to chack if the mean is different than 500, which could include both cases of >500mg and <500mg.

e.

The Type I error in this case is we reject the null hypothesis even though the true mean amount of acetaminophen in cold capsules is equal to 500 mg.

f.

The Type II error in this case is we fail to reject the null hypothesis even though the true mean amount of acetaminophen in cold capsules is different than 500 mg.

g.

Conclusion: The null hypothesis can be rejected as there is sufficient evidence to support the claim that the mean amount of acetaminophen in cold capsules is different than 500 mg.

B. The Laban Party standard bearer claims that he is currently favored by more than one-half of his constituency.

a.

The claim is that proportion of voters supporting Laban party is more than half (or 0.5 or 50%)

b.

The null hypothesis is that proportion of voters supporting Laban party is less than or equal to 0.5 (or 50%)

c.

The alternate hypothesis is that proportion of voters supporting Laban party is more than 0.5 (or 50%)

d.

The test is right tailed, since we want to check if the proportion is greater than 0.5, which includes only the right tail of the distribution.

e.

The Type I error in this case is we reject the null hypothesis even though the true proportion of voters supporting Laban party is less than or equal to 0.5 (or 50%).

f.

The Type II error in this case is we fail to reject the null hypothesis even though the true proportion of voters supporting Laban party is more than 0.5 (or 50%).

g.

Conclusion: The null hypothesis can be rejected as there is sufficient evidence to support the claim that proportion of voters supporting Laban party is more than half.

C. The Department of Education claims that over 2% of all adults are enrolled in school full-time.

a.

The claim is that proportion of adults enrolled in school full-time is greater than 2%.

b.

The null hypothesis is that proportion of adults enrolled in school full-time is less than or equal to 2%.

c.

The alternate hypothesis is that proportion of adults enrolled in school full-time is greater than 2%.

d.

The test is right tailed, since we want to check if the proportion is greater than 0.02, which includes only the right tail of the distribution.

e.

The Type I error in this case is we reject the null hypothesis even though the true proportion of adults enrolled in school full-time is less than or equal to 2%.

f.

The Type II error in this case is we fail to reject the null hypothesis even though the true proportion of adults enrolled in school full-time is greater than 2%.

g.

Conclusion: The null hypothesis can be rejected as there is sufficient evidence to support the claim that proportion of adults enrolled in school full-time is greater than 2%.

D.

that fewer than 10% of cars on the road have a design that benefits from higher octane gasoline.

a.

The claim is that proportion of cars on the road have a design that benefits from higher octane gasoline is less than 10%.

b.

The null hypothesis is that proportion of cars on the road have a design that benefits from higher octane gasoline is greater than or equal to 10%.

c.

The alternate hypothesis is that proportion of cars on the road have a design that benefits from higher octane gasoline is less than 10%.

d.

The test is left tailed, since we want to check if the proportion is less than 0.10, which includes only the left tail of the distribution.

e.

The Type I error in this case is we reject the null hypothesis even though the true proportion of cars on the road have a design that benefits from higher octane gasoline is greater than or equal to 10%.

f.

The Type II error in this case is we fail to reject the null hypothesis even though the true proportion of cars on the road have a design that benefits from higher octane gasoline is less than 10%.

g.

Conclusion: The null hypothesis can be rejected as there is sufficient evidence to support the claim that proportion of cars on the road have a design that benefits from higher octane gasoline is less than 10%.