Question

For the following claim, find the null and alternative hypotheses, test statistic, critical value, and draw conclusion. Assume that a simple random sample has been selected from a normally distributed population.

Claim: the mean IQ score of statistics professors is less than 127.
Sample data: n = 28, x = 125, s = 13. The significance level is a = 0.05

Answer 1

Claim is that the mean IQ score of statistics professors is less than 127

so, it is a left tailed hypothesis

Using TI 84 calculator

press stat then tests then Ttest

enter the data set

press calculate

we get

test statistic = -0.814

p value = 0.2114

t critical = T.INV(alpha,df)

where df = n-1 = 28-1 = 27 and alpha = 0.05

t critical = -1.703

t statistic is not less than t critical, so we failed to reject the null hypothesis

therefore, there is insufficient evidence to conclude that the mean IQ score of statistics professors is less than 127.