Question

100. We are interested in whether the proportions of female suicide victims for ages 15 to 24 are the same for the whites and the blacks races in the United States. We randomly pick one year, 1992, to compare the races. The number of suicides estimated in the United States in 1992 for white females is 4,930 . Five hundred eighty were aged 15 to 24 . The estimate for black females is 330 . Forty were aged 15 to 24 . We will let female suicide victims be our population.

Short answer

(a) The null hypothesis: $H_0:P_W=P_B$
(b) The alternate hypothesis: $H_0:P_W\ne P_B$
(c) The random variable is the proportion of white and black suicide victims between the ages of 15 and 24.
(d) For two proportions, normal.
(e) The test statistics $-0.1944$
(f) The $p$-value is $0.8458$.
(g)(i) $\alpha =0.05$
(ii) Decision: not to reject the null hypothesis.
(iii) Reason for Decision: $\alpha <p-$ value .
(iv) As a result: There is insufficient data to infer that the proportions of white and black female suicide victims, aged 15 to 24, are different at the $5\%$significance level.

Step-by-step solution

Given information

Let, the number of suicides estimated in the United States in $1992$ for white females is $4,930$. Five hundred eighty were aged $15$ to $24$.

Explanation

(a) The null hypothesis is indicated as:
$H_0:P_W=P_B$
(b) The alternate hypothesis is indicated as:
$H_0:P_W\ne P_B$
(c) The random variable is the proportion of white and black suicide victims between the ages of 15 and 24.
(d) For two proportions, normal.
(e) To determine the test static as follows:
To access the stat list editor, click STAT and then 1.

Then ENTER all values the OUTPUT will be:

Hence, the test statistics is $-0.1944$.

Explanation

(f) The $p$-value from the output is determined as $0.8458$.
(g) Obtain a clear picture of the situation using the information from the last task.
The horizontal axis should be clearly labelled and scaled, and the region(s) corresponding to the $p$-value should be shaded on the graph.

(i) $\alpha =0.05$
(ii) Decision: not to reject the null hypothesis.
(iii) Reason for Decision: $\alpha <p-$ value .
(iv) As a result: There is insufficient data to infer that the proportions of white and black female suicide victims, aged 15 to 24, are different at the $5\%$significance level.