Exam 8: Estimating Single Population Parameters

Sampling error is the difference between a statistic computed from a sample and the corresponding parameter computed from the population.

The Wisconsin Dairy Association is interested in estimating the mean weekly consumption of milk for adults over the age of 18 in that state.To do this,they have selected a random sample of 300 people from the designated population.The following results were recorded: = 34.5 ounces s = 7.9 ounces Given this information,if the leaders wish to estimate the mean milk consumption with 90 percent confidence,what is the approximate margin of error in the estimate?

In determining the required sample size when estimating a population proportion,it is necessary to start with some idea of what that proportion is.

In an effort to estimate the mean dollars spent per visit by customers of a food store,the manager has selected a random sample of 100 cash register receipts.The mean of these was $45.67 with a sample standard deviation equal to $12.30.Assuming that he wants to develop a 90 percent confidence interval estimate,which of the following is the margin of error that will be reported?

A regional hardware chain is interested in estimating the proportion of their customers who own their own homes.There is some evidence to suggest that the proportion might be around 0.70.Given this,what sample size is required if they wish a 90 percent confidence level with a margin of error of ± .025?

When determining the sample size for a proportion,if you have no previous information available to estimate π,then the best value to use is π = 0.5.

A major tire manufacturer wishes to estimate the mean tread life in miles for one of its tires.It wishes to develop a confidence interval estimate that would have a maximum sampling error of 500 miles with 90 percent confidence.A pilot sample of n = 50 tires showed a sample standard deviation equal to 4,000 miles.Based on this information,the required sample size is:

The chamber of commerce in a beach resort town wants to estimate the proportion of visitors who are repeat visitors.From previous experience they believe the portion is in the vicinity of 0.5 and they want to estimate the proportion to within ± 0.03 percentage points with 95 percent confidence.The sample size they should use is:

Which of the following statements applies to a point estimate?

The concept of margin of error applies directly when estimating a population mean,but is not appropriate when estimating a population proportion.

The t-distribution is used for the critical value when estimating a population proportion when the standard deviation of the population is not known.

The chamber of commerce in a beach resort town wants to estimate the proportion of visitors who are repeat visitors.Suppose that they have estimated that they need a sample size of n=16,577 people to achieve a margin of error of ± .01 percentage points with 99 percent confidence,but this is too large a sample size to be practical.How can they reduce the sample size?

The manager of the local county fair believes that no more than 30 percent of the adults in the county would object to a fee increase to attend the fair if it meant that better entertainment could be secured.To estimate the true proportion,he has selected a random sample of 200 adults.The manager will use a 90 percent confidence level.Assuming his assumption about the 30 percent holds,the margin of error for the estimate will be approximately ± .169.

In a recent report to the supply chain manager in a major electronics company,the report writer stated that with 90 percent confidence,the manufacturing lead time for a critical part is between 3.34 hours and 4.14 hours.Based on this information,the margin of error for this estimate is ± .80 hours.

When using a 95 percent confidence interval for a mean,the area in the upper tail of the distribution that is outside the interval is 5 percent.

The makers of weight loss product are interested in estimating the mean weight loss for users of their product.To do this,they have selected a random sample of n = 9 people and have provided them with a supply of the product.After six months,the nine people had an average weight loss of 15.3 pounds with a standard deviation equal to 3.5 pounds.The upper limit for the 90 percent confidence interval estimate for the population mean is approximately 17.47 pounds.

An educational organization in California is interested in estimating the mean number of minutes per day that children between the age of 6 and 18 spend watching television per day.A previous study showed that the population standard deviation was 21.5 minutes.The organization selected a random sample of n = 200 children between the age of 6 and 18 and recorded the number of minutes of TV that each person watched on a particular day.The mean time was 191.3 minutes.If the leaders of the organization wish to develop an interval estimate with 98 percent confidence,what would be the upper and lower limits of the interval estimate?

A statement in the newspaper attributed to the leader of a local union stated that the average hourly wage for union members in the region is $13.35.He indicated that this number came from a survey of union members.If an estimate was developed with 95 percent confidence,we can safely conclude that this value is within 95 percent of the true population mean hourly wage.

A study has indicated that the sample size necessary to estimate the average electricity use by residential customers of a large western utility company is 900 customers.Assuming that the margin of error associated with the estimate will be ± 30 watts and the confidence level is stated to be 90 percent,what was the value for the population standard deviation?

Under what circumstances would you wish to select a pilot sample?