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

Step-by-step 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 :-

$z=\dfrac{x-\mu_0}{\dfrac{\sigma}{\sqrt{n}}}$

$\Rightarrow\ z=\dfrac{140-135}{\dfrac{13}{\sqrt{23}}}\\\\\Rightarrow\ z=1.84455058589\approx1.8446$

Hence, the value of test statistic =  1.8446