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%.

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