Exam 8: Interval Estimation

A researcher is interested in determining the average number of years employees of a company stay with the company. If past information shows a standard deviation of 7 months, what size sample should be taken so that at 95% confidence the margin of error will be 2 months or less?

From a population that is normally distributed, a sample of 25 elements is selected and the standard deviation of the sample is computed. For the interval estimation of $\mu$ , the proper distribution to use is the

After computing a confidence interval, the user believes the results are meaningless because the width of the interval is too large. Which one of the following is the best recommendation?

A sample of 196 bags of sugar produced by Domain sugar producers showed an average of 2 pounds and 2 ounces with a standard deviation of 7 ounces. a.At 95% confidence, compute the margin of error and explain what it shows. b.Determine a 95% confidence interval for the weight of the population of bags of sugar produced by the company. Give the answer in ounces and at least two significant digits. c.The bags of sugar produced are supposed to contain 2 pounds of sugar, but the company allows 2% higher or lower than the 2 pounds. Have they reached their desired goal? Explain why or why not by giving numerical facts.

You are given the following information obtained from a sample of 5 observations taken from a population that has a normal distribution. 94 72 93 54 77 Develop a 98% confidence interval estimate for the mean of the population.

Exhibit 8-3 The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took these 100 customers to check out was 3.0 minutes. It is known that the standard deviation of the population of checkout times is one minute. -Refer to Exhibit 8-3. The standard error of the mean equals

Exhibit 8-4 In order to estimate the average electric usage per month, a sample of 81 houses was selected, and the electric usage was determined. Assume a population standard deviation of 450-kilowatt hours. -Refer to Exhibit 8-4. If the sample mean is 1,858 KWH, the 95% confidence interval estimate of the population mean is

A statistician employed by a consumer testing organization reports that at 95% confidence he has determined that the true average content of the Uncola soft drinks is between 11.7 to 12.3 ounces. He further reports that his sample revealed an average content of 12 ounces, but he forgot to report the size of the sample he had selected. Assuming the standard deviation of the population is 1.28, determine the size of the sample.

In order to determine an interval for the mean of a population with unknown standard deviation a sample of 61 items is selected. The mean of the sample is determined to be 23. The number of degrees of freedom for reading the t value is

A statistician selected a sample of 16 accounts receivable and determined the mean of the sample to be $5,000 with a standard deviation of $400. He reported that the sample information indicated the mean of the population ranges from $4,739.80 to $5,260.20. He neglected to report what confidence coefficient he had used. Based on the above information, determine the confidence coefficient that was used. Assume the population has a normal distribution.

A random sample of 81 children with working mothers showed that they were absent from school an average of 6 days per term with a standard deviation of 1.8 days. Provide a 95% confidence interval for the average number of days absent per term for all the children.

Many people who bought X-Game gaming systems over the holidays have complained that the systems they purchased were defective. In a sample of 1200 units sold, 18 units were defective. a.Determine a 95% confidence interval for the percentage of defective systems. b.If 1.5 million X-Games were sold over the holidays, determine an interval for the number of defectives in sales.

In a random sample of 100 observations, = 0.2. The 95.44% confidence interval for P is

Exhibit 8-3 The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took these 100 customers to check out was 3.0 minutes. It is known that the standard deviation of the population of checkout times is one minute. -Refer to Exhibit 8-3. With a .95 probability, the sample mean will provide a margin of error of

The monthly incomes from a random sample of workers in a factory are shown below. a.Compute the standard error of the mean (in dollars). b.Compute the margin of error (in dollars) at 95% confidence. c.Compute a 95% confidence interval for the mean of the population. Assume the population has a normal distribution. Give your answer in dollars.

A sample of 60 students from a large university is taken. The average age in the sample was 22 years with a standard deviation of 6 years. Construct a 95% confidence interval for the average age of the population.

From a population that is not normally distributed and whose standard deviation is not known, a sample of 6 items is selected to develop an interval estimate for the mean of the population ( $\mu$ ).

If we want to provide a 95% confidence interval for the mean of a population, the confidence coefficient is

If the standard deviation of the lifetime of a vacuum cleaner is estimated to be 300 hours, how large of a sample must be taken in order to be 97% confident that the margin of error will not exceed 40 hours?

Exhibit 8-6 A sample of 75 information system managers had an average hourly income of $40.75 with a standard deviation of $7.00. -Refer to Exhibit 8-6. The standard error of the mean is