Question

1. In an August 2012 Gallup survey of 1,012 randomly selected U.S. adults (age 18 and over), 53% said that they were dissatisfied with the quality of education students receive in kindergarten through grade 12. The bootstrap distribution (based on 5,000 samples) is provided.

 

a). Would it be appropriate to use the normal distribution to construct the confidence interval in this situation? Explain briefly.

b). The standard error from the bootstrap distribution is SE = 0.016. Use the normal distribution to construct and interpret a 99% confidence interval for the proportion of U.S. adults who are dissatisfied with the education students receive in kindergarten through grade 12. 

Round to three decimal places.

2. A small university is trying to monitor its electricity usage. For a random sample of 

30 weekend days (Saturdays and Sundays), the student center used an average of 94.26 kilowatt hours (kWh) with standard deviation 43.29. For a random sample of 60 weekdays, (Monday - Friday), the student center used an average of 112.63 kWh with standard deviation 32.07.

1. Test, at the 5% level, if significantly more electricity is used at the student center, on average, on weekdays than weekend days. Remember to check the conditions, identify the hypotheses, define your parameter, find the test statistic, find the p-value, and give a conclusion in context.

1. Construct a 95% confidence interval for the difference in mean electricity use at the student center between weekdays and weekend days. Use two decimal places in your margin of error.

3. In a survey conducted by the Gallup organization September 6-9, 2012, 1,017 adults were asked "In 

  general, how much trust and confidence do you have in the mass media - such as newspapers, TV,   

  and radio - when it comes to reporting the news fully, accurately, and fairly?" Of the 1,017 

  respondents, 214 said they had "no confidence at all."

a). Test, at the 5% level, if this sample provides evidence that the proportion of U.S. adults who have no confidence in the media differs significantly from 25%. Verify that the sample size is large enough to use the normal distribution to compute the p-value for this test and include all of the details of the test.

b). Verify that the sample size is large enough to use the normal distribution to construct a confidence interval for the proportion of U.S. adults who have no confidence in the media.

c). Construct a 90% confidence interval for the proportion of U.S. adults who have no confidence in the media. Round the margin of error to three decimal places.

d). What sample size is needed to reduce the margin of error to 1%?