PLEASE HELP!!

STAT 308 Homework #6

1. According to the US Bureau of Labor Statistics publication News, self-employed persons with home-based businesses work a mean of 23 hours per week at home with a standard deviation of 10 hours.

1. Identify the population and variable.
2. For samples of size 100, find the mean and standard deviation of all possible sample mean hours worked per week at home.
3. Repeat part (b) for samples of size 1000.
4. What effect has increasing the sample size on the mean and standard deviation of all possible sample mean hours worked per week at home?

2. In 1905 R Pearl published the article "Biometrical Studies on Man. I. Variation and Correlation in Brain Weight". According to the study, brain weights of Swedish men are normally distributed with a mean of 1.4 kg and a standard deviation of 0.11 kg.

1. Determine the sampling distribution of the sample mean for samples of size 3.
2. Repeat part (a) for samples of size 12.
3. That is, for parts (a) and (b) discuss the distribution, mean and standard deviation of the sample means for the different sample sizes.
4. Use Excel to construct graphs similar to those shown in Fig 7.4 on page 321 in the textbook. Hand in your excel output and show the data you used to construct the plots, as well as the plots (see instructions below). No excel, no credit.
5. Do you need to assume that brain weights of Swedish men are normally distributed to answer parts (a) and (b)? Explain your answer

3. Refer to question (2) in this assignment.

1. Determine the percentage of all samples of three Swedish men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.40 kg. That is, between 1.3 and 1.5 kgs.
2. Repeat part (a) for samples of size 12

4. Do Exercise 7.80, parts (a) and (b), on page 326 in the textbook.