Answer to Question #89793 in Statistics and Probability for cccc

Question

A researcher is interested in whether people are able to identify emotions correctly when they
are extremely tired. It is known that, using a particular method of measurement, the accuracy
ratings of people in the general population (who are not extremely tired) are normally
distributed with a mean of 82 and a variance of 64. In the present study, however, the
researcher arranges to test 36 people who had no sleep the previous night. The mean accuracy
for these 36 individuals was 84. Using the 0.05 alpha level for a one-tailed test, what should the
researcher conclude for the sample?

Answer 1

$H_0:\;\mu=82\\ H_a:\;\mu>82\\ Test\;statistic:\;z=\frac{84-82}{\frac{8}{\sqrt{36}}}=1.5\\ P-value:\;p=0.0668\\ Since\;the\;P\;value\;is\;greater\;than\;0.05\;fail\\to\;reject\;the\;null\;hypothesis.$