Question

Pathological gambling is an impulse-control disorder. The National Gambling Impact Study Commission randomly selected 2719 adults and found that 246 were pathological gamblers. Is there evidence to conclude that more than 8% of the adult population are pathological gamblers as claimed by the American Psychiatric Association? Use α = 0.05 to test the claim.

Answer 1

If the calculated z value is greater than 1.645, reject the null hypothesis; otherwise, if it is less than or equal to 1.645, fail to reject the null hypothesis.

- Sample proportion (
`\( \hat{p} \)`): 246/2719

- Sample size (n): 2719

- Claimed proportion by APA (
`p_0`): 0.08

- Critical value for (α = 0.05) in a one-tailed test: approximately 1.645

Test Statistic Formula:

`\[ z = (\hat{p} - p_0) / √((p_0(1 - p_0) / n)) \]`

Substitute the values:

`\[ z = ((246 / 2719) - 0.08) / √((0.08 * (1 - 0.08) / 2719)) \]`

Now, calculate the numerator and denominator separately and then plug them into the formula.

If (z) is greater than 1.645, you would reject the null hypothesis. If (z) is less than or equal to 1.645, you would fail to reject the null hypothesis.