# BUS 210 BUS210 Module 8 Homework Solution (AAU Online)

**PART I: APPLICATION**

1.There are 2,000 eligible voters in a precinct. 500 of the voters are randomly selected and asked whether they planned to vote for the Democratic incumbent or the Republican challenger. Of the 500 surveyed, 350 said they would vote for the Democratic incumbent. Using the 0.99 confidence coefficient, what are the confidence limits for the proportion that plan to vote for the Democratic incumbent?

2.A random sample of 85 group leaders and supervisors revealed that they worked an average of 6.5 years before being promoted. The population standard deviation was 1.7 years. Using the 0.95 degree of confidence, what is the confidence interval for the population mean?

3.A student wanted to construct a 95% confidence interval for the average age of students in her statistics class. She randomly selected 9 students. Their average age was 19.1 years with a standard deviation of 1.5 years. What is the best point estimate for the population mean?

4.The American Auto Association reports the mean price per gallon of regular gasoline is $3.10 with a population standard deviation of $0.20. Assume a random sample of 16 gasoline stations is selected and their mean cost for regular gasoline is computed. What is the standard error of the mean in this experiment?

5.LongLast Inc. produces car batteries. The mean life of these batteries is 60 months. The distribution of the battery life closely follows the normal probability distribution with a standard deviation of 8 months. As part of its testing program, LongLast tests a sample of 25 batteries. What is the standard error of the mean?

6.A population consists of the following four values: 8, 10, 12, and 16. From this population, there are 6 different samples of size 2. The means of the 6 samples of size 2 are: 9, 10, 12, 11, 13, and 14. Compute the mean of the distribution of the sample means and the population mean. What is true about the two values?

7.A university has 1000 computers available for students to use. Each computer has a 250 gigabyte hard drive. The university wants to estimate the space occupied on the hard drives. A random sample of 100 computers showed a mean of 115 gigabytes used with a standard deviation of 20 gigabytes. What is the standard error of the mean?

8.In practice, researchers collect a sample of size "n" and compute point estimates of population parameters. How can sampling error be reduced?

9.A research firm conducted a survey to determine the mean amount people spend at a popular coffee shop during a week. They found the amounts spent per week followed a normal distribution with a population standard deviation of $4. A sample of 49 customers revealed that the mean is $25. What is the 95 percent confidence interval estimate of µ?

10.A local grocery store wants to estimate the mean daily number of gallons of milk sold to customers. Assume the number of gallons sold follows the normal distribution with a population standard deviation of 5.10 gallons. A random sample of 60 days shows that the mean daily number of gallons sold is 10.00. What is the point estimate of the population mean?

11.A local health care company wants to estimate the mean weekly elder day care cost. A sample of 10 facilities shows a mean of $250 per week with a standard deviation of $25. What is the 90 percent confidence interval for the population mean?

12.A company's headquarters is located in downtown Chicago. The company is interested to know the mean driving time of its employees if they require their employees to start working at 6:00 am. Fifty employees are randomly sampled over four weeks and asked to record their driving time. The mean driving time is 35 minutes with a standard deviation is 10 minutes. What is the 98 percent confidence interval for the population mean?

13.A university wants to determine the proportion of students who use a cash card to pay at the university food service. Out of 100 students surveyed, 65 students use a cash card. Estimate the value of the population proportion.

14.The Nile Superstore is conducting a survey of consumer preferences for a new wireless e-book reader. A sample of 160 people reveals that 120 would buy the new reader. Estimate the value of the population proportion.

15.A population is estimated to have a standard deviation of 25. We want to estimate the population mean within 2, with a 95 percent level of confidence. How large a sample is required?

16.Sugar is packaged in 16 ounce bags. If 42 bags are sampled, with a mean of 15.95 ounces and a standard deviation of 0.4 ounces, what is the 99 percent confidence interval estimate of the population mean?

17.Thirty-six items are randomly selected from a population of 150 items. The sample mean is 25 and the sample standard deviation 3. What is the finite population correction factor?

18.Forty-nine items are randomly selected from a population of 200 items. The sample mean is 30 and the sample standard deviation 16. What is the 99 percent confidence interval for the population mean?

19.A local politician wants an estimate of the proportion of the population who support her fiscal policies. She wants the estimate to be within .06 of the true proportion. Assume a 95 percent level of confidence. The politician's advisors estimated the proportion supporting her fiscal policy to be .60. How large of a sample is required?

20.25 percent of tourists going to Atlantic City to gamble spend more than $500. The Atlantic City Chamber of Commerce wants to update this percentage. For the new study, the estimate should be within 1% of the population proportion with a 90 percent confidence level. What is the necessary sample size?

**PART II: CASE STUDY**

**PART III: JOURNAL ACTIVITY**