1. A survey to 52 students taking an introductory statistics class. One professo
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Question
1.A survey to 52 students taking an introductory statistics class. One professor hypothesized that women enter graduate school at an earlier age than men. To test this hypothesis a two independent sample t-test was utilized based on the survey data from 52 students. Note that the investigators did not believe the hypothesis from the professor so they utilized a two-tailed alternative hypothesis. Use the output in the Appendix to answer these questions.
Are the variances of age homogenous (equal) between males and females? Provide the justification (i.e. things in the SAS output) for your answer.
b. What is the test statistic for the two-sample t-test? Give the actual number.
c. Based on a confidence interval (CI) provided in the output, does mean age differ by gender? Provide the CI and justification for your answer.
d. Based on a p-value provided in the output, does mean age differ by gender? Provide the p-value and justification for your answer.
e. Does this data support the professor’s hypothesis that women enter graduate school earlier than men? Why or why not?
Use this data to answer the questions
Question 1
The TTEST Procedure
Variable: age
gender N Mean Std Dev Std Err Minimum Maximum
Female 21 27.0952 7.4088 1.6167 19.0000 48.0000
Male 31 29.8387 11.1925 2.0102 20.0000 62.0000
Diff (1-2) -2.7435 9.8550 2.7853
gender Method Mean 95% CL Mean Std Dev 95% CL Std Dev
Female 27.0952 23.7228 30.4677 7.4088 5.6682 10.6988
Male 29.8387 25.7333 33.9442 11.1925 8.9441 14.9608
Diff (1-2) Pooled -2.7435 -8.3378 2.8509 9.8550 8.2457 12.2505
Diff (1-2) Satterthwaite -2.7435 -7.9250 2.4381
Method Variances DF t Value Pr > |t|
Pooled Equal 50 -0.98 0.3294
Satterthwaite Unequal 49.989 -1.06 0.2927
Equality of Variances
Method Num DF Den DF F Value Pr > F
Folded F 30 20 2.28 0.0457
Explanation / Answer
b. What is the test statistic for the two-sample t-test? Give the actual number.
-0.98 for pooled
-1.06 for satterthwaite
c. Based on a confidence interval (CI) provided in the output, does mean age differ by gender?
the values are -8.33 and 2.85
as this range contains zero(which signifies no difference) , hence the results are not signficant
Provide the CI and justification for your answer.
d. Based on a p-value provided in the output, does mean age differ by gender? Provide the p-value and justification for your answer.
the p value is 0.3294. considering an alpha of 0.05 , as the p value is not less than 0.05 , hence we fail to reject the null hypothesis and conclude that results are not sigificant
e. Does this data support the professor’s hypothesis that women enter graduate school earlier than men? Why or why not?
as the difference of means is not signficant hence we cant conclude that women enter graudate school earlier than mean.
also as shoewn above , the confidence interval includes both negative and positve values for the difference of means .
Hence this doesnt necesaarily mean that women enter earlier than men in graduate school.
Please note that we can answer only 4 subparts of a question at a time.
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