9. The Scenario The California Taxpayers' Association wanted to know how Californians felt about several new taxes. To learn how Californians felt about these new taxes, they gave a survey asking about the new taxes. One of the questions was: Do you believe the new gas taxes will drive the average price of gas to over $5.00 per gallon this summer? They survey 1113 California adults, 813 of which responded to the survey. Of the respondents, 427 answered yes, they think the new taxes will drive gas prices to over $5.00 per gallon. The Questions Compute a 95% confidence interval for the proportion of California adults who believe the new gas taxes will drive the price of gas to over $5.00 per gallon. You may use an app to do the computations. You must show all your computations and/or a screenshot of any app used. Please use your work answer the following. What is p-hat? Please give your answer exact to three decimal places. What is the standard error for this interval? Please give your answer exact to four decimal places. What is the confidence interval? Please give your answer in proper interval format exact to four decimal places. Put your interval into context of the scenario. A reporter claimed in an article that at least 47% of Californians believe that gas price will go over $5.00 per gallon due to the new gas taxes. Does your confidence interval provide evidence that the reporter is correct? Provide an argument based on your calculations that it does or does not provide such evidence.
The California Taxpayers' Association wanted to know how Californians felt about several new taxes. To learn how Californians felt about these new taxes, they gave a survey asking about the new taxes. One of the questions was: Do you believe the new gas taxes will drive the average price of gas to over $5.00 per gallon this summer?
They survey 1113 California adults, 813 of which responded to the survey. Of the respondents, 427 answered yes, they think the new taxes will drive gas prices to over $5.00 per gallon.
The Questions
Compute a 95% confidence interval for the proportion of California adults who believe the new gas taxes will drive the price of gas to over $5.00 per gallon. You may use an app to do the computations. You must show all your computations and/or a screenshot of any app used. Please use your work answer the following.
- What is p-hat? Please give your answer exact to three decimal places.
- What is the standard error for this interval? Please give your answer exact to four decimal places.
- What is the confidence interval? Please give your answer in proper interval format exact to four decimal places.
- Put your interval into context of the scenario.
- A reporter claimed in an article that at least 47% of Californians believe that gas price will go over $5.00 per gallon due to the new gas taxes. Does your confidence interval provide evidence that the reporter is correct? Provide an argument based on your calculations that it does or does not provide such evidence.
A nationwide study of American Homeowners revealed that 65% of homeowners have one or more lawn mowers. The Stihl lawn equipment manufacturer, located in Virginia Beach, believes the estimate is too low for households in that city.
They survey 392 homeonwers in Virginia Beach, 309 of which responded to the survey. Of the respondents, 218 said that they one or more lawn mowers.
The head of marketing for Stihl claims that the percentage of homeowners in Virginia Beach is greater than 65%.
The QuestionsConduct a hypothesis test at a 95% confidence level (alpha=.05) to test the claim made by head of marketing for Stihl. You may use an app to do the test, if you wish. Include all work and screenshots of any app used. Use the results of your hypothesis test to answer the following questions.
- What are your null and alternative hypotheses? Be sure to use appropriate notation and justify your choice of the alternative hypothesis from the context of the problem.
- What is the p-hat? Show computations and give p-hat exact to three decimal.
- What is the p-value of your test?
- What is the conclusion of your hypothesis test? Include statistical justification for your conclusion.
- Does the hypothesis test support the claim of head of marketing for Stihl? Why or why not?
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