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For the Week 4 Complete assignment, solve each problem and answer each question that corresponds with it. Explain how you arrived at the answer for each problem. The total word count for your assignment should be a minimum of 1200 words.

1. The following data show the costs charged by a tax preparation service for a random sample of 15 tax returns. 

     a. Using a 98% confidence interval, estimate the average cost of the service for preparing a tax return for a customer.       b. What is the margin of error for this sample?       c. Verify your result using Excel.       d. What assumptions are necessary for this analysis?

2. The makers of compact fluorescent light bulbs (CFL) claim the bulbs use 75% less energy and last 10 times longer than incandescent bulbs. A 16-watt CFL (equivalent to a 60-watt incandescent) has a rated lifetime of 8,000 hours. To test this claim, a random sample of 50 CFLs was drawn, and the average life of a bulb was determined to be 7,960 hours. Assume the standard deviation for the life of CFL bulbs is 240 hours.       a. Does this sample provide enough evidence to support the claim that CFLs average 8,000 hours with 95% confidence?       b. What is the margin of error for this sample using a 95% confidence interval?       c. Verify your result using Excel.

3. Certain advertisers would like to estimate the proportion of viewers who spend the majority of their television time watching alone. The consensus is that this percentage has been increasing over the years due to the increased number of television sets in U.S. households.       a. Determine the sample size needed to construct a 90% confidence interval with a margin of error no more than 5% to estimate the true proportion of viewers who watch television alone.       b. What impact would a pilot sample that showed that 38% of viewers spend the majority of

their television time watching alone have on your results?

4. To design a new advertising campaign, Volkswagen would like to estimate the proportion of drivers of the new VW Beetle who are women. In a random sample of 250 Beetle owners, 140 of them were women.       a. Construct a 95% confidence interval to estimate this proportion.       b. What is the margin of error for this sample?

5.   Verizon Wireless would like to estimate the average number of text messages received by American teenagers per month. A random sample of 60 teenaged customers was selected. The sample average was 2,272 messages per month, and the sample standard deviation was 953 messages per month. Construct confidence intervals with the following confidence levels:       a. 90%       b. 95%       c. 99%

6. According to statista.com, the average room rate for a New York City hotel in 2016 was $337. Suppose the Chamber of Commerce of New York City would like to test if this rate has changed recently by randomly sampling 40 room rates. The mean of this sample was found to be $351.20. Assume the population standard deviation is $55. Using a = 0.05, answer the following.       a. State the null and alternative hypothesis.       b. What conclusions can be drawn for this test?       c. Determine the p-value for this test and interpret its meaning.  

7. According to the Glassdoor.com, each job opening on average attracted 250 résumés in 2016. You know that the job market improved in 2017 compared to 2016, which means that more people will likely be switching jobs but also fewer unemployed workers remain in the labor market. To find out which trend is stronger, you take a random sample of 20 employers in your area and ask them to report how many résumés they received in 2017 for each job opening. Here are their answers:

Using a = 0.05, answer the following:       a. State the null and alternative hypotheses.       b. Does this sample provide enough evidence to suggest that the number of résumés that were received in 2017 has changed?       c. Determine the precise p-value for this test using Excel.       d. What assumptions need to be made to perform this analysis?

8.   Smart meters are a special type of electrical meter that monitors the usage of electricity and communicates that information back to the utility company. According to a report by the Energy Information Administration from December 2017, 47% of homes in the United States were equipped with smart meters in 2016. To test if this percentage has changed, a random sample of 200 U.S. residences was recently selected, and it was found that 96 of them were equipped with smart meters. Using a = 0.05, answer the following:       a. State the null and alternative hypothesis.       b. Based on this sample, do we have enough evidence to conclude that the percentage of homes in the United States equipped with smart meters has changed since 2016?       c. Determine the p-value for this test and interpret its meaning.

9. Baggage fees charged by airlines have received much attention recently as the industry has looked for ways to increase revenue without directly in-creasing fares. American Airlines would like to investigate if the average number of bags checked per flight fell after the company implemented fees for checking them. The following table shows the average numbers of checked bags per flight for a random sample of Boeing 737 domestic flights both before and after the fees were implemented. The population standard deviations and sample sizes are also indicated.

     a. Perform a hypothesis test using a = 0.10 to determine if the average number of checked bags decreased after the checked-baggage fees were administered.       b. Determine the p-value and interpret the results.       c. Construct a 90% confidence interval to estimate the difference in the average number of checked bags per flight before and after the fees were implemented.

10. During the 2007–2008 decline in the housing mar-ket, it appeared that the average size of a newly constructed house fell. To investigate this trend, the square footages of a random sample of houses built in 2008 were compared to houses built in 2018. A random sample of 45 homes built in 2008 had a sample mean of 2,462.3 square feet and a sample standard deviation of 760.8 square feet. A random sample of 40 homes built in 2018 had a sample mean of 2,257.0 square feet and a sample standard deviation of 730.2 square feet. Assume that the population variances for the square footages of houses built in these two years are equal.       a. Using a = 0.05, perform a hypothesis test to determine if the average home constructed in 2010 was larger than a home built in 2018.       b. Construct a 95% confidence interval to estimate the average difference in the square footages of new homes constructed in these two years. Inter-pret your result.       c. Determine the precise p-value using Excel and interpret the results.       d. What assumptions need to be made in order to perform this procedure?