A college professor randomly selects 25 freshmen to study the mathematical background of the incoming freshman class. The average SAT score of these 25 students is 565 and the standard deviation is estimated to be 40. Using this information, can this professor fully believe that the average test score of all incoming students is larger than 550 at a 5% level of significance?

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Elena Ray · Accepted Answer

From the given information,Sample size (n) = 25Sample mean =565Sample standard deviation (s) = 40.Level of significance (α) = 0.05Claim: professor fully believes that the average test score of all incoming students is larger than 550 at a 5% level of significance:Hypothesis testH0:μ=550H1:μ&amp;gt;550Test statistics:t=x―−μsn=565−5504025=1.875Thus, test statistics is 1.875t-critical value:tα2n−1=t0.05225−1=1.7109Conclusion:Since, t-statistic value is more than t-critical value that is, 1.875&amp;gt;1.7109. Thus, it implies that reject null hypothesis at the given level of significance because t-statistical value is fall in the rejection region.Hence, it can be concluded that the claim made by professor is significant therefore he fully believes that the average test score of all incoming students is larger than 550 at a 5% level of significance is true.

A college professor randomly selects 25 freshmen to study the mathematical background of the incomin

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