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# Problems on Sampling distributions

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Sampling Distributions. See attached file for full problem description.

11. Appliance magazines provided estimates of the life expectancy of household appliances. A simple random sample of 10 VCRs shows the following useful life in years.

6.5 8.0 6.2 7.4 7.0 8.4 9.5 4.6 5.0 7.4

A. Develop a point estimate of the population mean life expectancy for VCRs.
B. Develop a point estimate of the population standard deviation for life expectancy of VCRs.

13. A Louis Harris poll used a survey of 1008 adults to learn about how people feel about the economy. Responses were as follows.

595 adults The economy is growing
81 adults The economy is shrinking.

Develop a point estimate of the following population parameters.
A. The proportion of all adults who feel the economy is growing.
B. The proportion of all adults who feel the economy is staying about the same
C. The proportion of all adults who feel the economy is shrinking

17. Suppose a simple random sample of size 50 is selected from a population with =10.
Find the value of the standard error of the mean in each of the following cases (uses the finite population correction factor if appropriate).

A. The population size in infinite
B. The population size is N = 50,000.
C. The population size is N = 5000
D. The population size is N = 500.

21. The College Board American College Testing Program reported a population mean SAT score of µ = 1020. Assume that the population standard deviation is = 100.

A. What is the probability that a random sample of 75 students will provide a sample mean SAT score within 10 of the population mean?

B. What is the probability a random sample of 75 students will provide a sample mean SAT score within 20 of the population mean?