The claim is that the IQ scores of statistics professors are normally​ distributed, with a mean greater than 116. A sample of 20 professors had a mean IQ score of 121 with a standard deviation of 11. Find the value of the test statistic.

Answer:   t= 2.032Step-by-step explanation:Given : Sample size : [tex]n=20[/tex]Sample mean : [tex]\overline{x}=121[/tex]Standard deviation : [tex]\sigma= 11[/tex]Claim : The IQ scores of statistics professors are normally​ distributed, with a mean greater than 116. Let [tex]\mu [/tex] be the mean scores of statistics professors.Then the set of hypothesis for the given situation will be :-[tex]H_0:\mu\leq116\\\\H_1:\mu>116[/tex]As the alternative hypothesis is right tailed , thus the test would be right tail test.Since the sample size is less than 30, therefore the test would be t-test .The test statistics for the given situation will be :-[tex]t=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex][tex]\Rightarrow\ t=\dfrac{121-116}{\dfrac{11}{\sqrt{20}}}=2.03278907045\approx2.032[/tex]Hence, the value of the test statistic : t= 2.032