Part A-
Question 1: You want to rent an unfurnished one-bedroom apartment for next semester. The mean monthly rent for a random sample of 10 apartments advertised in the local paper is $640. Assume that the standard deviation is $90. Find a 95% confidence interval for the mean monthly rent for unfurnished one-bedroom apartments available for rent in this community. Do this problem by hand and scan/take a picture of your work and upload (You may also type your solution up)
Question 2: Hypotheses. Translate each of the following research questions into appropriate null hypothesis (Ho) and alternative hypothesis (Ha). Write your answers in a word document.
a) Census Bureau data show that the mean household income in the area served by a shopping mall is $62,500 per year. A market research firm questions shoppers at the all to find out whether the mean household income of mall shoppers is higher than the general population.
b) Last year, your company's service technicians took an average of 2.6 hours to respond to trouble calls from business customers who had purchased service contracts. Do this year's data, show a different average response time.
Question 3: Do this problem by hand and scan/take a picture of your work and upload (You may also type your solution up). You may use a calculator or excel to compute the mean of the sample.
c) Your company sells exercise clothing and equipment on the internet. To design clothing, you collect data on the physical characteristics of your different types of customers. Here are the weights for a sample of 24 male runners. Assume that these runners can be viewed as a random sample of your potential customers. The weights are expressed in kilograms:
67.8 61.9 63.0 53.1 62.3 59.7 55.4 58.9
60.9 69.2 63.7 683 64.7 65.6 56.0 57.8
66.0 62.9 53.6 65.0 55.8 60.4 69.3 61.7
Assume that the population standard deviation is σ = 4.5 kg. Based on this confidence interval, does a test of Ho: μ=61.3 kg
Hα: μ≠61.3 kg
Reject Ho at the 5% significance level?
Part B-
Question 1: An office building in New York uses thousands of fluorescent light bulb each year. The brand of bulb it currently uses has a mean life of 900 hours. A manufacturer claims that its new brand of bulbs, which cost the same as the brand the office building currently uses, has a mean life of more than 900 hours. The university has decided to purchase the new brand if, when tested, the test evidence supports the manufacturer's claim at the .05 significance level. Suppose 64 bulbs and the sample has a mean of 920 hours and a standard deviation of 80 hours.
- What are the null hypothesis and the alternative hypothesis?
- Should the office building purchase the new brand of florescent bulbs? (i.e. test your hypothesis using a z-test).