Question

How much does a sleeping bag cost? Let’s say you want a sleeping bag that should keep you warm in temperatures from 20oF to 45oF. A random sample of prices ($) for sleeping bags in this temperature range was taken from Backpacker Magazine: Gear Guide (Vol. 25, Issue 157, No. 2.)

80      90        100      120      75      37      30        23        100      100

105      95        105      60      110      120      95        90        60        70

Find the mean x ( round to two decimals places)

Find the sample standard deviation   s    ( round to two decimals places)

Find a 90% confidence interval for the mean price µ of all summer sleeping bags.

2. Over the past few months, an adult patient has been treated for tetany (severe muscle spasms.) This condition is associated with total calcium level below 6 mg/dl . Reference: Manual of Laboratory and Diagnostics Tests by F. Fischbach). Recently, the patient’s total calcium tests gave the following readings in mg/dl

9.3       8.8       10.1     8.9       9.4       9.8

10.0     9.9       11.2     12.1

Find the mean x      ( round to two decimals places)

Find the sample standard deviation   s     (round to two decimals places)

Find a 99.9% confidence interval for the mean calcium level.

3.A random sample of 40 students taken from a university showed that their mean GPA is 2.94 and the standard deviation of their GPAs is .30. Construct a 99% confidence interval for the mean GPA of all students at this university.

4.According to a study done by Dr. Martha S. Linet and others, the mean duration of the most recent headache was 8.2 hours for a sample of 5055 females 12 through 29. Make a 95% confidence interval for the mean duration of all headaches for all 12 to 29-year-old females. The standard deviation for this sample is 2.4 hours.

5. According to a survey conducted by USA TODAY, 73.2% of the workers in the United States drive alone to work. Assume that this survey is based on a random sample of 1000 US workers.

Find a 95% confidence interval for all workers in the United States who drive alone to work.

Answer 1

I have provided the solution for the first question.

It is a t-distribution problem.

The solution is provided in images below: