A study conducted several years ago reported that 21 percent of public accountants changed companies within 3 years. The American Institute of CPA's would like to update the study. They would like to estimate the population proportion of public accountants who changed companies within 3 years with a margin of error of 3% and a 95% level of confidence.

a. To update this study, the files of how many public accountants should be studied?

b. How many public accountants should be contacted if no previous estimates of the population proportion are available?

You plan to conduct a survey to find what proportion of the workforce has two or more jobs. You decide on the 95 percent confidence level and state that the estimated proportion must be within 2 percent of the population proportion. A pilot survey reveals that 5 of the 50 sampled hold two or more jobs. How many in the workforce should be interviewed to meet your requirements?

A population is estimated to have a standard deviation of 10. We want to estimate the population mean within 2, with a 95 percent level of confidence. How large a sample is required?

Dylan Jones kept careful records of the fuel efficiency of his new car. After the first nine times he filled up the tank, he found the mean was 23.4 miles per gallon with a sample standard deviation of 0.9 mpg. a.Compute the 95 percent confidence interval for his mpg.b. How many times should he fill his gas tank to obtain a margin of error below 0.1 mpg?

Dr. Susan Benner is an industrial psychologist. She is currently studying stress among executives of Internet companies. She has developed a questionnaire that she believes measures stress. A score above 80 indicates stress at a dangerous level. A random sample of 15 executives revealed the following stress level scores.

$$\begin{array}{lllllllllllllll} 94 & 78 & 83 & 90 & 78 & 99 & 97 & 90 & 97 & 90 & 93 & 94 & 100 & 75 & 84 \end{array}$$

a. Find the point estimate of the population mean. b. Construct a $95 \%$ confidence level for the population mean. c. According to Dr. Benner's test, is it reasonable to conclude that the mean stress level of Internet executives is 80 ? Explain.

A survey of 36 randomly selected iPhone owners showed that the purchase price has a mean of $\$ 650$ with a sample standard deviation of $\$ 24$. a. What is the point estimate of the population mean? b. What is the point estimate of the population standard deviation? c. What is the standard error of the sample mean? d. Compute the $95 \%$ confidence interval to estimate the population mean. e. How many users need to be sampled to estimate the population mean price with $95 \%$ confidence and a $\$ 10$ marqin of error?

Bob Nale is the owner of Nale’s Quick Fill. Bob would like to estimate the mean number of gallons of gasoline sold to his customers. Assume the number of gallons sold follows the normal distribution with a population standard deviation of 2.30 gallons. From his records, he selects a random sample of 60 sales and finds the mean number of gallons sold is 8.60. a. What is the point estimate of the population mean? b. Develop a 99 percent confidence interval for the population mean. c. Interpret the meaning of part (b).

Marty Rowatti recently assumed the position of director of the YMCA of South Jersey. He would like some current data on how long current members of the YMCA have been members. To investigate, suppose he selects a random sample of 40 current members.The mean length of membership of those included in the sample is 8.32 years and the standard deviation is 3.07 years. a. What is the mean of the population? b. Develop a 90 percent confidence interval for the population mean. c.The previous director, in the summary report she prepared as she retired, indicated the mean length of membership was now “almost 10 years.” Does the sample information substantiate this claim? Cite evidence.

According to a poll of 25 randomly selected judges working for the state of Florida, their average hourly pay (benefits included) was $65.00. The$6.25/hour sample standard deviation. With the help of this, develop a 99% confidence interval for the population mean wage (including benefits) for these employees.

We want to estimate the population mean within 5, with a 99 percent level of confidence. The population standard deviation is estimated to be 15. How large a sample is required?

Past surveys reveal that $30 \%$ of tourists going to Las Vegas to gamble spend more than $\$ 1,000$. The Visitor's Bureau of Las Vegas wants to update this percentage. a. How many tourists should be randomly selected to estimate the population proportion with a $90 \%$ confidence level and a $1 \%$ margin of error. b. The Bureau feels the sample size determined above is too large. What can be done to reduce the sample? Based on your suggestion, recalculate the sample size.

Past surveys reveal that 30 percent of tourists going to Las Vegas to gamble spend more than $1,000. The Visitor’s Bureau of Las Vegas wants to update this percentage. a. The new study is to use the 90 percent confidence level. The estimate is to be within 1 percent of the population proportion. What is the necessary sample size? b. The Bureau feels the sample size determined above is too large. What can be done to reduce the sample? Based on your suggestion, recalculate the sample size.

Netflix is considering a new romcom (romantic comedy) series. Before making a final decision, the producers design an experiment to estimate the proportion of viewers who would watch the series. A random sample of 400 viewers was selected and asked to watch the first two episodes. After viewing the episodes, 250 viewers indicated they would watch the new series. a. Estimate the value of the population proportion of people who would watch the new series. b. Develop a $99 \%$ confidence interval for the population proportion of people who would watch the new series. c. Interpret your findings.

According to a poll of 25 randomly selected judges working for the state of Florida, their average hourly pay (benefits included) was $65.00. The$6.25/hour sample standard deviation. With the help of this, find what is the population mean? What is the best estimate of the population mean?