Question

A researcher is interested in whether people become worse at identifying emotions correctly when they are tired. It is known that, using a particular method of assessment, the accuracy ratings of people in the general population (who are not extremely tired) are normally distributed with a mean of 82 and a standard deviation of 20. In the present study, however, the researcher arranges to test 50 people who had no sleep the previous night to see if they will do worse. The mean accuracy for these 50 individuals was 78. Using the .05 level, test whether the null hypothesis should be rejected.

Answer 1

Researcher wants to know whether the sample mean provides sufficient evidence to conclude that the mean is less than 82 or not. So, it is a left tailed hypothesis

Population standard deviation is known and sample size is greater than 30, so we will use normal distribution

given that

z statistic =

using z distribution table, check -1.4 in the left most column and 0.01 in the top row, then select the intersecting cell, we get

p value = 0.0787

it is clear that the p value is greater than significance level of 0.05, so we failed to reject the null hypothesis as the result is insignificant

we can conclude that there insufficient evidence to prove that the mean is less than 82