Question

A publisher reports that 79% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 150 found that 72% of the readers owned a laptop. Find the value of the test statistic. Round your answer to two decimal places.

Answer 1

The value of the test statistic is -1.91.

Explanation:

We are given that a publisher reports that 79% of their readers own a laptop. A random sample of 150 found that 72% of the readers owned a laptop.

A marketing executive wants to test the claim that the percentage is actually different from the reported percentage.

Let p = population % of readers who own a laptop

SO, Null Hypothesis,
`H_0` : p = 79% {means that the percentage is same as that of the reported percentage}

Alternate Hypothesis,
`H_a` : p
`\\eq` 79% {means that the percentage is actually different from the reported percentage}

The test statistics that will be used here is One-sample z proportion statistics;

T.S. =
`\frac{\hat p-p}{\sqrt{(\hat p(1- \hat p))/(n) } }` ~ N(0,1)

where,
`\hat p` = % of the readers who owned a laptop in a sample of 150 readers = 72%

n = sample of readers = 150

So, test statistics =
`\frac{0.72-0.79}{\sqrt{(0.72(1- 0.72))/(150) } }`

= -1.91

Therefore, the value of the test statistic is -1.91.