years of education.
1. Using appropriate software, produce a scatterplot of wage rates
against years of education using your sample. Compute the sample
correlation and comment on whether you agree with Amy. [2
marks]
2. Test whether there is a statistically significant linear
association between wages and years of education, showing all your
steps and clearly stating your conclusion. [4 marks] Amy sets up a
regression model to investigate whether wage rates depend
positively on years of education.
3. Write down Amy’s regression model taking care to define your
notation clearly. Using ap- propriate software, estimate the
regression model and report your results. [2 marks]
4. Use your regression results to give a one-sentence
interpretation of the regression slope estimate. [2 marks]
5. Test whether years of education is an effective predictor of
wage rates in the regression model you have estimated in question
3. Make sure to report your null and alternative hypotheses, the
test statistic, decision rule, and conclusion to the test. [2
marks] Amy suspects that men are paid more than women, on average.
To investigate this claim statistically, you will use a hypothesis
test.
6. Set up the null and alternative hypotheses taking care to
define your notation clearly. [2marks]
7. Using the ‘Shift Groups’ randomization method in Statkey,
produce a dotplot of the random- ization distribution (with at
least 2,000 samples) of the appropriate sample statistic. Carry out
the hypothesis test using the randomization distribution and state
your conclusion. [2 marks]
8. Verify that the Central Limit Theorem applies in this case,
carry out the same hypothesis test using the appropriate
approximation and state your conclusion. Briefly compare these
results to your findings in question 7. [2 marks]
9. Does the evidence suggest that men are paid more than women
as a consequence of their gender? Explain. [2 marks]
- Questions Amy Believes That Wage Rates Depend Positively On Years Of Education 1 Using Appropriate Software Produce A 1 (92.79 KiB) Viewed 13 times
fx Wage 4 A 4.Z U 4.75 1 12 6.94 0 18 41 8.5 0 8 3.75 0 8 8 0 15 4.85 0 10 45 5 0 14 46 3 1 16 47 8 19 7.33 0 13 7.33 0 14 50 8 0 12 6.25 0 7 52 5.26 1 12 2.75 1 12 3.33 0 12 3 1 12 5.25 14 7.25 0 16 9 3.25 1 59 2.51 1 12 60 7.29 0 12 61 6.25 0 12 62 7.5 0 17 0 15 0 13 1 10 10 1 12 67 3.25 3.63 0 11 5 1 12 6.9 0 16 71 3.6 1 15 7.69 1 16 73 6.71 0 12 74 12.5 0 15 75 5.25 1 76 3.25 Sheet1 55 55 33 00 B 6.25 2.7 5.14 1 in w 12 21 1 11 + D E LL G H J K > L 11
fx Wage A A 12.5 0 15 5.25 1 12 3.25 1 11 4.63 0 18 5.1 1 15 5.71 1 12 7 2.25 1 3.25 1 12 3.5 1 14 7.29 0 84 4.3 0 10 9.5 0 10 2 1 13 2 + 87 4 0 12 88 5.5 0 11 8.18 0 18 90 8.82 0 16 7.5 0 12 3.5 1 12 4.75 0 12 5 1 14 5.07 0 12 5.71 1 14 3.65 0 10 1 12 0 12 0 6 0 12 74 75 76 728 97 98 11.11 99 5.14 100 4.82 101 5.14 102 103 104 105 106 107 108 109 110 111 Sheet1 B U + D E LL G H I J K H 11