Question: According to a union agreement, the mean income for all senior-level workers in a large service company equals $500 per week. A representative of a women's group decides to analyze whether the mean income ? for female employees matches this norm. For a simple random sample of nine female employees, ? = $410 and s = 90. (a) Test whether the mean income of female employees differs from $500 per week. State the null and alternative hypotheses, and calculate the test statistic (show your work) and P-value. State your conclusion.  Edit

Answer: Null hypothesis H0: The population mean income for women equals $500 per week, µ=$500

Alternative hypothesis Ha:The mean income for women does not equal $500 per week, µ is different from $500

SE =90/Sqrt(9) =30
The margin of error is thus 1.96*30 = 58.8 and we find that the Confidence Interval at 95% is:
[ 410 – 58.8 , 410 + 58.8 ] = [ 351.2 , 468.8 ]
$500 does not fall in the confidence interval therefore we can reject the null hypothesis that the population average wage for women is different from $500.  Edit