Statistics 216

stats216.docx

Home >Business & Finance homework help >Economics homework help >Statistics 216

Hypothesis Testing with Two Samples

Due: wed 6

Directions: This assignment must be typed. Please have all of the pages of your homework stapled together. In the upper right corner please have your name. You are to work on this assignment individually.

1. You are to use the State Gas Tax 2019 data available in my pick-up folder (under ..) 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. Please print a copy of your excel output.

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. You are going to use the housing data available in my pick-up folder (under …)). 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 available in my pick up folder. 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).

4. Using the same housing data in question 3, please conduct an F-test to compare whether there has been a change in variance between now and 5 years ago in total housing cost. Is it reasonable to conclude that the variance has changed? Explain. To answer this question, you need to conduct an F-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 (but not raw data).