Question

(6 pts) A psychologist who needs two groups of students for a learning experiment decides to select a random sample of female college students and male college students. Before the experiment, the psychologist administers an IQ test to both groups to determine if there is a significant difference in their mean IQ scores. The population standard deviation for this IQ test is know to be for both female and male populations. If the sample mean IQ score of the female students is and the sample mean IQ score for the male students is , can the psychologist conclude that there is a significant difference in the mean IQ score of both groups at ? Let population 1 be female students and population 2 be male students.

Note that direction is not specified in this problem, and the population standard deviation is given. See Chapter 13.

(a) State the hypotheses:

   There is   Choose:    a negative difference    a positive difference    no difference    between the   Choose:    population proportion    population mean    sample mean    sample proportion       IQ score for female students and male students.

   The   Choose:    sample mean    sample proportion    population proportion    population mean       IQ score for female students   Choose:    is less than    is different than    is greater than    is the same as       the   Choose:    sample mean    sample proportion    population proportion    population mean       IQ score for male students.

(b) The correct symbol for mean of the sampling distribution is
A.
B.
C.
D.
E.
F.
G.
H.

(c) The value for the mean of the sampling distribution is:  .

(d) Choose the correct distribution
A. Chi-Square Distribution
B. T-Distribution
C. Normal Distribution

Why?
A. We are provided with for the two populations.
B. We are provided with and .
C. The size of n1 < 30 and n2 < 30
D. We are not provided with for the two populations.
E. n1p1, n1(1-p1), n2p2, and n2(1-p2) are all greater than 5.

(e) State the decision rule:

Choose:    Reject Ho and accept Ha    Reject Ha and accept Ho    Fail to reject Ha    at =  % if the p-value of the sample statistic is   Choose:    equal to 0.0001    less than or equal to 0.0001    greater than or equal to 0.0001    greater than or equal to 0.01    equal to 0.01    less than or equal to 0.01    .

(f) Experiment
Symbol of the sample statistic:
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.

Value of the sample statistic:    P-value of the sample statistic rounded to 4 decimal places:

(g) Conclusion
Choose:    Fail to reject Ha    Fail to reject Ho    Reject Ho and accept Ha    Reject Ha and accept Ho    at =  %

(h) Answer the question
Can the psychologist conclude that there is a significant difference in the mean IQ score of both groups?
A. No, because the mean IQ score for female students is significantly different than mean IQ score for male students.
B. Yes, because the mean IQ score for female students is significantly different than mean IQ score for male students.
C. Yes, because the mean IQ score for female students is not significantly different than mean IQ score for male students.
D. No, because the mean IQ score for female students is not significantly different than mean IQ score for male students.

(i) Type I Error
If a type I error were made in this test, it would mean
A. there is a significant difference in the population mean IQ scores for female students and male students, but we incorrectly failed to reject the null hypothesis.
B. there is no difference in the population mean IQ scores for female students and male students, but we incorrectly rejected the null hypothesis.
C. there is no difference in the population mean IQ scores for female students and male students, but we incorrectly failed to reject the null hypothesis.
D. there is a significant difference in the population mean IQ scores for female students and male students, but we incorrectly rejected the null hypothesis.

(j) Type II Error
If a type II error were made in this test, it would mean
A. there is no difference in the population mean IQ scores for female students and male students, but we incorrectly rejected the null hypothesis.
B. there is no difference in the population mean IQ scores for female students and male students, but we incorrectly failed to the null hypothesis.
C. there is a significant difference in the population mean IQ scores for female students and male students, but we incorrectly rejected the null hypothesis.
D. there is a significant difference in the population mean IQ scores for female students and male students, but we incorrectly failed to reject the null hypothesis.

Answer 1

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