Question

1. In the EAI sampling problem, the population mean is $51,300 and the population standard deviation is $5,000. When the sample size is n = 30, there is a 0.4161 probability of obtaining a sample mean within +/- $500 of the population mean. Use z-table.

1.1 What is the probability that the sample mean is within $500 of the population mean if a sample of size 60 is used (to 4 decimals)?

1.2 What is the probability that the sample mean is within $500 of the population mean if a sample of size 120 is used (to 4 decimals)?

2. The following data are from a simple random sample. 4, 9, 12, 7, 12, 16

2.1 What is the point estimate of the population mean?

2.2 What is the point estimate of the population standard deviation (to 1 decimal)?

3. Suppose a random sample of size 53 is selected from a population with = 10. Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate).

3.1 The population size is infinite (to 2 decimals).

3.2 The population size is N = 50,000 (to 2 decimals).

3.3 The population size is N = 5,000 (to 2 decimals).

3.4 The population size is N = 500 (to 2 decimals).

4. A population has a mean of 400 and a standard deviation of 60. Suppose a sample of size 100 is selected and is used to estimate . Use z-table.

4.1 What is the probability that the sample mean will be within +/- 7 of the population mean (to 4 decimals)? (Round z value in intermediate calculations to 2 decimal places.)

4.2 What is the probability that the sample mean will be within +/- 12 of the population mean (to 4 decimals)? (Round z value in intermediate calculations to 2 decimal places.)

Answer 1

The Standard Z table: