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 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.

2. 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 these runners can be viewed as a random sample of your potential customers. The weights are expressed in kilograms.

53.1
53.6
55.4
55.8
56
57.8
58.9
59.7
60.4
60.9
61.7
61.9
62.3
62.9
63
63.7
64.7
65
65.6
66
68.3
68.7
69.2
69.3
1483.9
mean 61.82916667


Find a 95% confidence interval for the mean weight of the population of all such runners, assuming that the population standard deviation is 4.5 kg

(a) calculate a 95% confidence interval for the mean weight of all such runners.
(b) Based on this confidence interval, does a test of
H0: m = 61.3 kg
Ha: m not = 61.3 kg
reject H0 at the 5% significance level?

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With a small sample size (less than 30 observations) people usually use a t distribution. (Historical fact: The Student t-distribution was developed by a guy who worked for Guinness, the makers of the famous stout and sponsors of the Book or World Records.)

The t distribution needs the observations to be normally distributed. In our case, we will assume that monthly rents follow a normal distribution. A t distribution has a number of degrees of freedom, and in...