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Miscellaneus Statistics Questions

1. Assume there are 20 homes in the Quail Creek area and 10 of them have a security system. Four homes are selected at random:

(a) What is the probability all four of the selected homes have a security system? (Round your answer to 4 decimal places.)
(b) What is the probability none of the four selected homes have a security system? (Round your answer to 4 decimal places.)
(c) What is the probability at least one of the selected homes has a security system? (Round your answer to 4 decimal places.)

2. A study was conducted to determine if there was a difference in the humor content in British and American trade magazine advertisements. In an independent random sample of 278 American trade magazine advertisements, 69 were humorous. An independent random sample of 194 British trade magazines contained 34 humorous ads.

(a) State the decision rule for .05 significance level: H0: πA = πB; H1: πA ≠ πB. (Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places.)
(b) Compute the value of the test statistic. (Do not round the intermediate values. Round your answer to 2 decimal places.)

3. According to a study by the American Pet Food Dealers Association, 62 percent of U.S. households own pets. A report is being prepared for an editorial in the San Francisco Chronicle. As a part of the editorial a random sample of 280 households showed 180 own pets. Does this data disagree with the Pet Food Dealers Association data? Use a 0.20 level of significance.

(a) State the null hypothesis and the alternate hypothesis. (Round your answers to 2 decimal places.)
(b) State the decision rule for 0.20 significance level. (Round your answers to 2 decimal places.)
(c) Compute the value of the test statistic. (Round your answer to 2 decimal places.)

4. A United Nations report shows the mean family income for Mexican migrants to the United States is $28,540 per year. A FLOC (Farm Labor Organizing Committee) evaluation of 28 Mexican family units reveals a mean to be $34,120 with a sample standard deviation of $10,050. Does this information disagree with the United Nations report? Apply the 0.01 significance level.

(a) State the null hypothesis and the alternate hypothesis.
(b) State the decision rule for .01 significance level. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)
(c) Compute the value of the test statistic. (Round your answer to 2 decimal places.)

5.As part of an annual review of its accounts, a discount brokerage selects a random sample of 27 customers. Their accounts are reviewed for total account valuation, which showed a mean of $34,900, with a sample standard deviation of $8,300.

What is a 95 percent confidence interval for the mean account valuation of the population of customers? (Round your answers to the nearest dollar amount. Omit the "$" sign in your response.)

95 percent confidence interval for the mean account valuation is between___ $ and____ $ ?

6. An important factor in selling a residential property is the number of people who look through the home. A sample of 17 homes recently sold in the Buffalo, New York, area revealed the mean number looking through each home was 26 and the standard deviation of the sample was 7 people.

Develop a 90 percent confidence interval for the population mean. (Round your answers to 2 decimal places.)

Confidence interval for the population mean is between____ and____ ?

7. During a national debate on changes to health care, a cable news service performs an opinion poll of 490 small-business owners. It shows that 48 percent of small-business owners do not approve of the changes.

(a) Develop a 90 percent confidence interval for the proportion opposing health care changes. (Round your answers to 4 decimal places.)

Confidence interval for the proportion_____ and_____ .

8. In the Department of Education at UR University, student records suggest that the population of students spends an average of 5.80 hours per week playing organized sports. The population's standard deviation is 2.80 hours per week. Based on a sample of 100 students, Healthy Lifestyles Incorporated (HLI) would like to apply the central limit theorem to make various estimates.

(a) Compute the standard error of the sample mean. (Round your answer to 2 decimal places.)
(b) What is the chance HLI will find a sample mean between 5 and 6.6 hours? (Round z and standard error values to 2 decimal places and final answer to 4 decimal places.)
(c) Calculate the probability that the sample mean will be between 5.5 and 6.1 hours. (Round z and standard error values to 2 decimal places and final answer to 4 decimal places.)

9. Keith's Florists has 19 delivery trucks, used mainly to deliver flowers and flower arrangements in the Greenville, South Carolina, area. Of these 19 trucks, 6 have brake problems. A sample of 5 trucks is randomly selected. What is the probability that 2 of those tested have defective brakes? (Round your answer to 4 decimal places.)

10. According to a government study among adults in the 25- to 34-year age group, the mean amount spent per year on reading and entertainment is $2,080. Assume that the distribution of the amounts spent follows the normal distribution with a standard deviation of $480. (Round z-score computation to 2 decimal places and your final answer to 2 decimal places. Omit the "%" sign in your response.)

(a) What percent of the adults spend more than $2,375 per year on reading and entertainment?
(b) What percent spend between $2,375 and $3,225 per year on reading and entertainment?
(c) What percent spend less than $1,175 per year on reading and entertainment?

$2.19