The mean amount of life insurance per household is $110 000. This distribution is positively skewed. The standard deviation of the population is $40 000.

1. A random sample of 50 households revealed a mean of $112 000. What is the standard error of the mean?

2. Suppose that you selected 50 samples of households. What is the expected shape of the distribution of the sample mean?

3. What is the likelihood of selecting a sample with a mean of at least $112 000?

4. What is the likelihood of selecting a sample with a mean of more than $100 000?

5. Find the likelihood of selecting a sample with a mean of more than $100 000 but less than $112 000.

The manufacturer of a new line of ink jet printers would like to include as part of its advertising the number of pages a user can expect from a print cartridge. A sample of 10 cartridges revealed the following number of pages printed.

1. What is the point estimate of the population mean?

2. Develop a 95 percent confidence interval for the population mean.

Passenger comfort is influenced by the amount of pressurization in an airline cabin. Higher pressurization allows a closer-to-normal environment and a more relaxed flight. A study by an airline user group recorded the corresponding air pressure on 30 randomly chosen flights. The study revealed a mean equivalent pressure of 8000 feet with a standard deviation of 300 feet.

1. Develop a 99 percent confidence interval for the population mean equivalent pressure.

2. How large a sample is needed to find the population mean within 25 feet at 95 percent confidence?

Passenger comfort is influenced by the amount of pressurization in an airline cabin. Higher pressurization allows a closer-to-normal environment and a more relaxed flight. A study by an airline user group recorded the corresponding air pressure on 30 randomly chosen flights. The study revealed a mean equivalent pressure of 8000 feet with a standard deviation of 300 feet.

1. Develop a 99 percent confidence interval for the population mean equivalent pressure.

2. How large a sample is needed to find the population mean within 25 feet at 95 percent confidence?

3. The post anesthesia care area (recovery room) at St. Luke’s Hospital was recently enlarged. The hope was that with the enlargement the mean number of patients per day would be more than 25. A random sample of 15 days revealed the following numbers of patients.

4.  

5. At the .01 significance level, can we conclude that the mean number of patients per day is more than 25? Estimate the p-value and interpret it.