Question

The claim is that the IQ scores of statistics professors are normally​ distributed, with a mean greater than 135. A sample of 23 professors had a mean IQ score of 140 with a standard deviation of 13. Find the value of the test statistic.

Answer 1

Answer: 1.8446

Explanation:

Given claim :
`\mu>\mu_0,\text{ where }\mu_0=135`

Sample size :
`n=23`

Sample mean :
`\overline{x}=140`

Standard deviation :
`\sigma = 13`

The test statistic for population mean is given by :-

`z=(x-\mu_0)/((\sigma)/(√(n)))`

`\Rightarrow\ z=(140-135)/((13)/(√(23)))\\\\\Rightarrow\ z=1.84455058589\approx1.8446`

Hence, the value of test statistic = 1.8446