Basic Statistics ECOE 1323

Spring 2006
Final Exam

Name:______ID Number:______

Instructions:

  1. Write your name and student ID.
  2. You have 2 hours
  3. This exam must be your own work entirely. You cannot talk to or share information with anyone.
  4. Show all your work. Partial credit will only be given where sufficient understanding of the problem has been demonstrated and work is shown.

Don't Write on This Table

Question / #1 / #2 / #3 / Total
Points

Section 1: Multiple-Choice

For each question in this section, circle the correct answer. (Problem is worth )

Questions 1-2 refer to the following information:

1-The height of Palestinian men aged 18 to 24 are approximately normally distribution with mean 68 inches and standard deviation 2.5 inches. Half of all young men are shorter than

a) / 65.5 inches / b) / 68 inches / c) / 70.5 inches

d)Can't tell, because the median height is not given.

2-Only about 5% of young men have heights outside the range

a) / 65.5 inches to 70.5 inches / b) / 63 inches to 73 inches
c) / a)60.5 inches to 75.5 inches / d) / 58 inches to 78 inches

Questions 3-4 refer to the following information:

3-A copy machine dealer has on the number x of copy machines at each of 89 customer locations and the number y of service calls in a month at each location. Summary calculationsgive. What is the slop of the least squares regression line of number of service calls on number of copiers?

a) / 1.56 / b) / 0.48 / c) / Non of these

d) Can't tell from the information given

4-About what percent of the variation in number of service calls is explained by the linear relation between number of service calls and the number of machines?

a) / 86% / b) / 93% / c) / 74% / d) / Non of these

e) Can’t tell from the information given

5-In a study of the effects of acid rain, random sample of 100 trees from a particular forest are examined. Forty percent of these show some signs of damage. Which of the following statements are correct?

a) / 40 % is a parameter

b) 40 % is a statistic

c) 40 % of all trees in this forest show some signs of damage

d) more than 40 % of the trees in this forest show some signs of damage

e) less than 40 % of the trees in this forest show some signs of damage

6-You play tennis regularly with a friend and from past experience you believe that the outcome of each match is independent. For any given match you have a probability of 0.6 of winning. The probability that you win the next tow matches is

a) / 0.36 / b) / 0.6 / c) / 0.4 / d) / 0.16 / e) / 1.2

Questions 6-7 refer to the following information:

6-In a large population of college students, 20 % of the students have experienced feelings of math anxiety. If you take a random sample of 10 students from this population, the probability that exactly 2 students have experienced math anxiety is

a) / 0.3020 / b) / 0.2634 / c) / 0.2013 / d) / 0.5 / e) / 1

7- The standarddeviation of the sample proportion of students who have experienced math anxiety is

a) / 0.0160 / b) / 0.1265 / c) / 0.2530 / d) / 1 / e) / 0.2070

8- You want to estimate the mean SAT score for a population of students with a 90% confidence interval. Assume that the population standard deviation is = 100. if you want the margin of error of the to be approximately 5, you will need a sample size of

a) / 33 / b) / 1083 / c) / 11 / d) / 1476

e) None of the above

Questions 9-10 refer to the following information:

9- A 95% confidence interval for the mean reading achievement score for a population of third grades is (44.2 , 54.2). The margin of error of this interval is

a) / 95% / b) / 5 / c) / 2.5 / d) / 54.2

e) The answer cannot be determined from the information given

10- The sample mean is

a) / 44.2 / b) / 54.2 / c) / 0.95 / d) / 49.2

e) The answer cannot be determined from the information given

11- Using the same set of data, you compute a 95% confidence interval and a 99% confidence interval. Which of the following statement is correct?

a) / The intervals have the same width / b) / The 99% interval is wider
c) / The 95 % interval is wider / c) / You cannot be determined which interval is wider unless you know n and s

12. You have measured the systolic blood pressure of a random sample of 25 employees of a company. A 95% confidence interval for the mean systolic blood pressure for the employees is computed to be (122,138). Which of the following statements gives a valid interpretation of this interval?

(a)About 95% of the samples of employees have a systolic blood pressure between 122 and 138.

(b)About 95% of the employees in the company have a systolic blood pressure between 122 and 138.

(c)If the sampling procedure were repeated many times, then approximately 95% of the resulting confidence intervals would contain the mean systolic blood pressure for employees in the company.

(d)If the sampling procedure were repeated many times, then approximately 95% of the sample means would be between 122 and 138.

For problems 13-14use the following information:

Parents in LakeWobegone think their children are smarter than average. To try and prove this they take a random sample of 2500 children from LakeWobegone and find their average IQ is 100.8 with a standard deviation of 15. The average IQ outside of LakeWobegone is 100.

13- The P-value of the test is

a) / 0.051 / b) / 0.012 / c) / 0.008 / d) / 0.004

14- A 90% confidence interval for the average IQ of Lake Wobegone children is

a) / (100.3,101.3) / b) / (100,101) / c) / (99.1,101.9) / d) / (93.4,108.2)

For problems 15-16, use the following information:

The shelf life of a carbonated beverage is of interest. Ten bottles are randomly selected and tested. The following results are obtained in days:

108 / 124 / 124 / 106 / 115 / 138 / 163 / 159 / 134 / 139

We want to test if the true mean shelf life is greater than 125 days.

15. The alternative hypothesis is

a) / / b) / / c) / / d) /

16. Which of the following is the test statistic?

a) / Z=0.31 / b) / T=0.97 / c) / Z=0.9 / d) / T=3.07

17. Which of the following is an example of a matched pairs design?

(a)A teacher compares the pre-test and the post-test scores of students.

(b)A teacher compares the scores of students using a computer-based method of instruction with the scores of other students using a traditional method of instruction.

(c)A teacher compares the scores of students in her class on a standardized test with national average score.

(d)A teacher calculates the average of scores of students on a pair of tests and wishes to see if this average is larger than 80%.

18. An airplane is only allowed a gross passenger weight of 8000 kg. If the weights of passengers traveling by air between Toronto and Vancouver have a mean of 78 kg and a standard deviation of 7 kg, the approximate probability that the combined weight of 100 passengers will exceed 8,000 kg is:

a) / 0.4978 / b) / 0.3987 / c) / 0.0044 / d) / 0.0022

19. A researcher wants to estimate the difference between the average response times (in minutes) of emergency 911 telephone calls for two cities. Based on a simple random sample of 75 calls from each city last month, the sample averages were 13 minutes for City 1 and 9 minutes for City 2. The sample standard deviations were 2.1 minutes for City 1 and 1.7 minutes for City 2.

A 90% confidence interval for the difference between the two population mean response times is

a) / (3.38, 4.62) / b) / (3.55, 4.45) / c) / (3.49, 4.51) / d) / (3.62, 4.60)

20. Which of the following statements about confidence intervals is INCORRECT?

(a)If we keep the sample size fixed, the confidence interval gets wider as we increase the confidence coefficient.

(b)A confidence interval for a mean always contains the sample mean.

(c)If we keep the confidence coefficient fixed, the confidence interval gets narrower as we increase the sample size.

(d)If the population standard deviation increases, the confidence interval decreases in width.

Section 1: Free Response Questions

Question #1: (6 Points)

A company wanted to know if attending a course on "how to be a successful salesperson" can increase the average sales of its employees. The company sent six of its salespersons to attend this course. The following table gives the week sales of these salespersons before and after they attended this course.

Before / 12 / 18 / 25 / 9 / 14 / 16
After / 18 / 24 / 24 / 14 / 19 / 20

Using the 1% significance level, can you conclude that the mean weekly sales for all salespersons increase as a result of attending this course? Assume that the population of paired difference has a normal distribution.

Question (2): (14 Points)

A political analyst was curious if younger adults were becoming more conservative. He decided to see if the mean age of registered Republicans was lower than that of registered Democrats. He selected an SRS of 128 registered Republicans from a list of registered Republicans and determined the mean age to be years, with a standard deviation years. He also selected an independent SRS of 200 registered Democrats from a list of registered Democrats and determined the mean age to be years, with a standard deviation years. Let represent the mean ages of the populations of all registered Republicans and Democrats, respectively. Suppose that the distributions of age in the populations of registered Republicans and of registered Democrats have the same standard deviation. Assume the pooled two-sample t-procedures are safe to use.

a. (2 Points) Compute the numerical value of the pooled estimator ofσ2,

b. (3 Points) Construct and 90% confidence interval for. Interpret your finding.

c. ( 2 Points) State H0 and Ha.

  • Ho:
  • Ha:

d. ( 3 Points) Calculate the test statistic.

e. ( 2 Points) Compute the P-value.

f. ( 2 Points) State your conclusion at level of significance.

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