Question

A simple random sample of 1088 adults between the ages of 18 and 44 is conducted. It is found that 274 of the 1088 adults smoke. Use a 0.05 significance level to test the claim that less than one-fourth of such adults smoke. Use P-value approach and determine conclusion.

Select one:

a. P-value = 0.889, fail to reject the alternative hypothesis

b. P-value = 0.444, fail to reject the null hypothesis

c. P-value = 0.444, reject the null hypothesis

d. P-value = 0.556, fail to reject the null hypothesis

e. P-value = 0.889, reject the alternative hypothesis

f. P-value = 0.556, reject the null hypothesis

Answer 1

Option d) P-value = 0.556, fail to reject the null hypothesis

Explanation:

We are given the following in the question:

Sample size, n = 1088

p = 0.25

Alpha, α = 0.05

Number of adults that smoke, x = 274

First, we design the null and the alternate hypothesis

`H_(0): p = 0.25\\H_A: p < 0.25`

This is a one-tailed(left) test.

Formula:

`\hat{p} = (x)/(n) = (274)/(1088) = 0.2518`

`z = \frac{\hat{p}-p}{\sqrt{(p(1-p))/(n)}}`

Putting the values, we get,

`z = \displaystyle\frac{0.2518-0.25}{\sqrt{(0.25(1-0.25))/(1088)}} = 0.139`

Now, we calculate the p-value from the table.

P-value = 0.556

Since the p-value is greater than the significance level, we fail to reject the null hypothesis and accept the null hypothesis.

Thus, there is not enough evidence to support the claim that less than one-fourth of adults between the ages of 18 and 44 smoke.