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

Step-by-step 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= $\hat{p}=\dfrac{x}{n}=\dfrac{462}{1491}=0.30985915493\approx0.31$

The test statistic for proportion is given by :-

$z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}$

Substitute all the values , we get

$z=\dfrac{0.31-0.30}{\sqrt{\dfrac{0.30(1-0.30)}{1491}}}\\\\=\dfrac{0.01}{\sqrt{0.000141}}\\\\=\dfrac{0.01}{0.011874342087}=0.84261497731\approx0.84$

Hence, the value of the test statistic = 0.84