Question

The Department of Labor would like to test the hypothesis that the average hourly wage for recent college graduates is less than $20. A random sample of 24 recent college graduates averaged $19.30 per hour with a standard deviation of $3.20 per hour. The Department of Labor would like to set ? = 0.10. Use the critical value approach to test this hypothesis. please either type this answer or be very careful to make your handwriting legible

Answer 1

Given that, sample size (n)= 24

sample mean =$19.30 per hour

sample standard deviation ( s ) = $3.20 per hour

Significance level = 0.10

Null and alternative hypotheses are,

Test statistic is,

Test statistic is t = -1.072

t-critical value at with degrees of freedom= n-1 = 24-1 =23 is, t^* = -1.319

Decision rule: since it is left-tailed test,

Reject H0, if test statistic is less than critical value = -1.319

Here, test statistic = -1.072 > t^* = -1.319

implies that we fail to reject the null hypothesis (H0)

Conclusion: There is not sufficient evidence to conclude that the average hourly wage for recent college graduates is less than $20.