Homework #9
Hypothesis Testing with Two Samples
Due: Wed. April 17, 2020
Directions: This homework assignment is due at the beginning of the class period on the date above. This assignment must be typed and submitted via Blackboard. You are to work on this assignment individually.
1. You are to use the State Gas Tax 2019 data available in our Blackboard under Homework Assignments. You are to test the hypothesis that the highest 10 states (from highest tax to lowest tax) are significantly higher in state tax on gasoline compared to the next 10 states listed (11-20). The first 10 states listed are Pennsylvania through Idaho and the next 10 states are Wisconsin to Indiana. Please double check your data for accuracy. For this analysis, you need to use the total tax rate per state. To test this, use a T-Test: Two-Sample Assuming Unequal Variances. It is found in the data analysis tab in excel. I want you to test your hypothesis at the 1% level (hint: you need to change alpha to 0.01). Is there any evidence that the first 10 states are significantly higher in state tax on gas compared to the next 10 states? Explain your findings, paying particular attention to differences between the two sample means and sample variances. You should plan on writing at least two or three sentences. To answer this question completely, please copy your excel output into a word document. (You do not need to include the raw data).
2. As part of the National Health and Nutrition Examination Survey conducted by the Department of Health and Human Services, self reported heights and measured heights were obtained for males aged 12-16. Listed below are the sample results.
Reported 68 71 63 70 71 60 65 64 54 63 66 72
Measured 67.8 69.9 64.9 68.3 70.3 60.6 64.5 67.0 55.6 64.2 65 70.8
Is there sufficient evidence to support the claim that there is a difference between the self-reported heights and measured heights of males aged 12-16? Use a 5% significance level.
You will need to use a T-Test: Paired Two sample for Means test in excel. First input the data into two columns. Second do to the Data tab, Data Analysis, then select T-Test: Paired Two sample for Means. Explain your results and include a copy of your excel output (not the raw data).
3. The amount of income spent on housing is an important component of the cost of living. The total costs of housing for homeowners might include mortgage payments, property taxes and utility costs (water, heat, electricity). An economist selected a sample of 20 homeowners in Denver and then calculated the total housing costs as a percent of monthly income, five years ago and now. The information is reported in the housing data set printed below. Is it reasonable to conclude that the percent is less now than five years ago? Explain.
To answer this question, you need to conduct a paired t-test, found under the data analysis tab in excel. You should test your hypothesis at the 5% level. Please write a brief answer to the above question (including explanation) and include your excel output (not raw data). You will not include homeowner identification numbers in your calculations.
Homeowner identification number Cost of Living 5 years ago Cost of Living now
1 17 10
2 20 39
3 29 37
4 43 27
5 36 12
6 43 41
7 45 24
8 19 26
9 49 28
10 49 26
11 35 32
12 16 32
13 23 21
14 33 12
15 44 40
16 44 42
17 28 22
18 29 19
19 39 35
20 22 12