Question

A publisher reports that 52% 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 180 found that 46% 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
`t = -1.61`

Explanation:

Central Limit Theorem

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean
`\mu = p` and standard deviation
`s = \sqrt{(p(1-p))/(n)}`

Our test statistic is:

`t = (X - \mu)/((\sigma)/(√(n)))`

In which X is the sample mean,
`\mu` is the expected mean,
`\sigma` is the standard deviation and n is the size of the sample.

A publisher reports that 52% of their readers own a laptop.

This means that
`\mu = 0.52`

Sample of 180:

Means that
`n = 180`

By the Central Limit Theorem:

`(\sigma)/(√(n)) = s = \sqrt{(0.52*0.48)/(180)} = 0.0372`

A random sample of 180 found that 46% of the readers owned a laptop.

This means that
`X = 0.46`

Find the value of the test statistic.

`t = (X - \mu)/(s)`

`t = (0.46 - 0.52)/(0.0372)`

`t = -1.61`

The value of the test statistic is
`t = -1.61`