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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.

Respuesta :

JeanaShupp

Answer: 1.8446

Step-by-step explanation:

Given claim : [tex]\mu>\mu_0,\text{ where }\mu_0=135[/tex]

Sample size : [tex]n=23[/tex]

Sample mean : [tex]\overline{x}=140[/tex]

Standard deviation : [tex]\sigma = 13[/tex]

The test statistic for population mean is given by :-

[tex]z=\dfrac{x-\mu_0}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

[tex]\Rightarrow\ z=\dfrac{140-135}{\dfrac{13}{\sqrt{23}}}\\\\\Rightarrow\ z=1.84455058589\approx1.8446[/tex]

Hence, the value of test statistic =  1.8446