Question

A survey of 35 people was conducted to compare their self-reported height to their actual height. The difference between reported height and actual height was calculated. You're testing the claim that the mean difference is greater than 0.7. From the sample, the mean difference was 0.95, with a standard deviation of 0.44. Calculate the test statistic, rounded to two decimal place

Answer 1

The test statistic is t = 3.36.

Explanation:

You're testing the claim that the mean difference is greater than 0.7.

At the null hypothesis, we test if the mean difference is of 0.7 or less, that is:

`H_0: \mu \leq 0.7`

At the alternate hypothesis, we test if the mean difference is greater than 0.7, that is:

`H_1: \mu > 0.7`

The test statistic is:

`t = (X - \mu)/((s)/(√(n)))`

In which X is the sample mean,
`\mu` is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.

0.7 is tested at the null hypothesis:

This means that
`\mu = 0.7`

A survey of 35 people was conducted to compare their self-reported height to their actual height.

This means that
`n = 35`

From the sample, the mean difference was 0.95, with a standard deviation of 0.44.

This means that
`X = 0.95, s = 0.44`

Calculate the test statistic

`t = (X - \mu)/((s)/(√(n)))`

`t = (0.95 - 0.7)/((0.44)/(√(35)))`

`t = 3.36`

The test statistic is t = 3.36.