Question

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

Answer 1

Answer: c. H0: p = 0.16; Ha: p ≠ 0.16

Explanation:

We know that ,

Null hypothesis is a statement about the population parameter(
`\mu , p, \sigma....`) and contains equality (=),≤ or ≥ signs.

Alternative hypothesis is also statement about the population parameter(
`\mu , p, \sigma....`) but against null hypothesis and contains signs < , > or ≠.

In the given situation , the parameter is p (population proportion).

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.

i.e. the point estimate of the population proportion(p) of the young adults who reported smoking at least twice a week or more is 0.16.

Now, the hypotheses to be tested for this study would be :

`H_0: p=0.16\\\\ H_a: p\\eq0.16`

Hence, the correct answer is c. H0: p = 0.16; Ha: p ≠ 0.16