Question

The claim is that the proportion of adults who smoked a cigarette in the past week is less than 0.30​, and the sample statistics include nequals1491 subjects with 462 saying that they smoked a cigarette in the past week. Find the value of the test statistic.

Answer 1

Answer: 0.84

Explanation:

let p be the population proportion of adults who smoked a cigarette in the past week.

As per given , we have

`H_a: p <0.30`

Sample size : n= 1491

The sample proportion of adults smoked a cigarette=
`\hat{p}=(x)/(n)=(462)/(1491)=0.30985915493\approx0.31`

The test statistic for proportion is given by :-

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

Substitute all the values , we get

`z=\frac{0.31-0.30}{\sqrt{(0.30(1-0.30))/(1491)}}\\\\=(0.01)/(√(0.000141))\\\\=(0.01)/(0.011874342087)=0.84261497731\approx0.84`

Hence, the value of the test statistic = 0.84