1. A researcher conducts a hypothesis test on a population proportion. Her null

Question

1. A researcher conducts a hypothesis test on a population proportion. Her null and alternative hypothesis are H0 : p = 0.4 and Ha : p < 0.4 . The test statistic and p-value for the test are z = ?3.01 and p?value = 0.0013 . For a significance level of ? = 0.05 , choose the correct conclusion regarding the null hypothesis.

Select one:
a. There is sufficient evidence to conclude that the population proportion is significantly less than 0.4.
b. There is sufficient evidence to accept the null hypothesis that the population proportion is equal to 0.4.
c. There is not sufficient evidence to reject the null hypothesis that the population proportion is equal to 0.4.
d. There is not sufficient evidence to conclude that the population proportion is significantly less than 0.4.

2. A researcher is wondering whether the smoking habits of young adults (18-25 years of age) in a certain city in the U.S. are different from the proportion of the general population of young adults in the U.S. A recent study stated that the proportion of young adults who reported smoking at least twice a week or more in the last month was 0.16. The researcher collected data from a random sample of 75 adults in the city of interest.

State the hypotheses to be tested for this study.

Select one:

a. H0: p = 0.16; Ha: p > 0.16

b. H0: p = 0.16; Ha: p =? 0.16

c. H0: p =? 0.16; Ha: p < 0.16

d. H0: p = 0.16; Ha: p < 0.16

Explanation / Answer

Ans:

1)Given that

H0 : p = 0.4 and Ha : p < 0.4 .

z = ?3.01 and p?value = 0.0013

As,p-value<0.05,we reject the null hypothesis.

Option a is correct.

There is sufficient evidence to conclude that the population proportion is significantly less than 0.4.

2)

Option b is correct.

H0: p = 0.16; Ha: p =? 0.16

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