It is known that the population mean for the Quantitative section of the GRE is 500, with a standard deviation of 100. In 2006, a sample of 400 students taking the GRE, whose family income was between $70,000 and $80,000, had a quantitative GRE score of 511. Perform a one-tailed hypothesis test to determine whether the group, whose family income was between

Question

It is known that the population mean for the Quantitative section of the GRE is 500, with a standard deviation of 100. In 2006, a sample of 400 students taking the GRE, whose family income was between $70,000 and $80,000, had a quantitative GRE score of 511. Perform a one-tailed hypothesis test to determine whether the group, whose family income was between
$70,000 and $80,000, scored significantly higher on average than the population.

10. What is the value of the test statistic?
a. .11
b. -.11
c. 2.2
d. -2.2
11. What is the p-value for the test statistic?
a. .4562
b. .5438
c. .0139
d. .9861
12. Using the significance level of .05, do the results lead to rejection of the null hypothesis?
Please describe what the results tell us about mean quantitative GRE scores for those with
a family income between $70,000 and $80,000.
 a. Yes, reject the null hypothesis. The mean quantitative GRE score for students, whose family income was between $70,000 and $80,000, is not significantly higher than then
the average quantitative GRE score for the population.
b. Yes, reject the null hypothesis. The mean quantitative GRE score for students, whose family income was between $70,000 and $80,000, is significantly higher than then the
average quantitative GRE score for the population.
c. No, do not reject the null hypothesis. The mean quantitative GRE score for students, whose family income was between $70,000 and $80,000, is not significantly higher than
then the average quantitative GRE score for the population.
d. No, do not reject the null hypothesis. The mean quantitative GRE score for students, whose family income was between $70,000 and $80,000, is significantly higher than then the average quantitative GRE score for the population.

PsyDAG · Answer

Ho: µ Pop = µ sample
Ha: µ Pop < µ sample

Z = (mean1 - mean2)/standard error (SE) of difference between means

SEdiff = √(SEmean1^2 + SEmean2^2)

SEm = SD/√n

If only one SD is provided, you can use just that to determine SEdiff.

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.