Question

Claim: Fewer than 95% of adults have a cell phone. In a reputable poll of 1063 adults, 87% said that they have a cell phone. Find the value of the test statistic

Answer 1

From the information given, it is found that the value of the test statistic is z = -11.97.

At the null hypothesis, it is tested if the proportion is of at least 95%, that is:

$H_0: p \geq 0.95$

At the alternative hypothesis, it is tested if the proportion is of less than 95%< that is:

$H_1: p < 0.95$

The test statistic is given by:

$z = \frac{\overline{p} - p}{\sqrt{\frac{p(1 - p)}{n}}}$

In which:

$\overline{p}$ is the sample proportion.

p is the value tested at the null hypothesis.

n is the sample size.

In this problem, we have that the parameters are:

$\overline{p} = 0.87, p = 0.95, n = 1063$.

Thus, the value of the test statistic is:

$z = \frac{\overline{p} - p}{\sqrt{\frac{p(1 - p)}{n}}}$

$z = \frac{0.87 - 0.95}{\sqrt{\frac{0.95(0.05)}{1063}}}$

$z = -11.97$

The value of the test statistic is z = -11.97.

A similar problem is given at https://brainly.com/question/24166849