Construting a 95% confidence interval for the population mean
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Question 1: Clothing for runners. Your company sells exercise clothing and equipment on the Internet. To design the 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 that these runners can be viewed as a random sample of your potential customers. The weight 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 68.3 64.7 65.6 56.0 57.8
66.0 62.9 53.6 65.0 55.8 60.4 69.3 61.7
Exercise 6.20 asks you to find a 95% confidence interval for the mean weight of the population of all such runners, assuming that the population standard deviation is sigma = 4.5 kg
(a) Give the confidence interval from that exercise or calculate the interval if you did not do the exercise.
(b) Based on this confidence interval, does a test of:
H0: u = 61.3 kg
Ha: u (does not = ) 61.3 kg
reject H0 at the 5% significance level?
(c) Would H0: u = 63 be rejected at the 5% level if tested against a two-sided alternative.
Question 2: Hypotheses. Translate each of the following research questions into appropriate H0 and Ha.
(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 question shoppers at the mall to find out whether the mean household income of mall shoppers is higher than that of 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: Apartment rental rates. 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 newspaper 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.
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Solution Summary
In this solution, you can find several examples of constructing a 95% confidence interval for the population mean. Also, we test hypotheses based on the constructed confidence interval.
Education
- BSc , Wuhan Univ. China
- MA, Shandong Univ.
Recent Feedback
- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"
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