Question

a medical study was investigating whether getting a flu shot actually reduced the risk of developing the flu. a hypothesis test is to be performed. which of the following statements is correct?
choose the correct answer below
a. a one - tailed test will be performed since the alternative hypothesis states that the parameter is not equal to the hypothesized value.
b. a two - tailed test will be performed since the alternative hypothesis states that the parameter is not equal to the hypothesized value.
c. a two - tailed test will be performed since the null hypothesis states that the parameter is not equal to the hypothesized valued.
d. a two - tailed test will be performed since the alternative hypothesis states that the parameter is less than they hypothesized value.
e. a one - tailed test will be performed since the alternative hypothesis states that the parameter is less than the hypothesized value.

Explanation:

A one - tailed test is used when the alternative hypothesis has a direction (e.g., \(H_1:\mu<\mu_0\) or \(H_1:\mu > \mu_0\)). A two - tailed test is used when \(H_1:\mu
eq\mu_0\). In this case, the medical study is investigating if getting a flu shot reduces the risk of developing the flu. The null hypothesis \(H_0\) would be that the flu shot has no effect (e.g., the proportion of getting flu with and without shot is the same, \(p_{shot}=p_{no - shot}\)) and the alternative hypothesis \(H_1\) is that the flu shot reduces the risk (e.g., \(p_{shot}

• Option A: Incorrect. A one - tailed test is for direction (not for \(H_1:\text{parameter}

eq\text{hypothesized value}\)).

• Option B: Incorrect. The alternative hypothesis here is not \(H_1:\text{parameter}

eq\text{hypothesized value}\) (which would be two - tailed), but \(H_1:\text{parameter}<\text{hypothesized value}\).

• Option C: Incorrect. The null hypothesis is \(H_0:\text{parameter}=\text{hypothesized value}\) (not \(H_0:\text{parameter}

eq\text{hypothesized value}\)), and the test type is determined by the alternative hypothesis.

• Option D: Incorrect. The alternative hypothesis is not \(H_1:\text{parameter}

eq\text{hypothesized value}\) (two - tailed), but \(H_1:\text{parameter}<\text{hypothesized value}\).

• Option E: Correct. The alternative hypothesis \(H_1\) (e.g., risk with shot is less than without shot) has a direction (\(<\)), so a one - tailed test is performed.

Answer:

E. A one - tailed test will be performed since the alternative hypothesis states that the parameter is less than the hypothesized value.