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Exam 4: Chapters 8, 9, & 10

Module by: Susan Dean, Barbara Illowsky, Ph.D.. E-mail the authors

Summary: Practice final exam for use with Collaborative Statistics (col10522) by Barbara Illowsky and Susan Dean.

  • Each question has exactly one best answer.
  • Each question is worth 3 points for a total of 54 points (4 bonus points possible).

Questions 1 – 3 refer to the following:

Last year, President Bush granted a tax-cut check to all income tax filers. In doing so, it was reported that he thought that at least 30% of the households would use the tax-cut check to increase spending. According to a report by the University of Michigan Research Center (Wall Street Journal, Feb. 26, 2002), 220 of the 1000 people surveyed said that the 2001 tax-cut check they received has led them to increase spending.

Exercise 1

The alternate hypothesis for this test is:

  • A. p>0.30
  • B. p>0.22
  • C. p>0.30
  • D. p>0.22

Exercise 2

A Type II error is to:

  • A. Conclude that the proportion of people that would use the tax-cut check to increase spending is less than 30% when in fact the proportion is at least 30%.
  • B. Conclude that the proportion of people that would use the tax-cut check to increase spending is at least 30% when in fact the proportion is less than 30%.
  • C. Conclude that the proportion of people that would use the tax-cut check to increase spending is less than 22% when in fact the proportion is at least 22%.
  • D. Conclude that the proportion of people that would use the tax-cut check to increase spending is at least 22% when in fact the proportion is less than 22%.

Exercise 3

Which of the following is the correct decision to make for the test?

  • A. Reject the null hypothesis.
  • B. Do not reject the null hypothesis.
  • C. The test is inconclusive.

Questions 4 – 6 refer to the following:

According to an article by George Will (San Jose Mercury News, Feb. 28, 2002), the average U.S. consumption per person per year of French Fries is 28 pounds. Suppose that you believe that the average in Santa Clara County is not 28 pounds. You randomly survey 50 people in this county. The sample average is 24 pounds with a sample standard deviation of 10 pounds. Conduct an appropriate hypothesis test.

Exercise 4

This test is:

  • A. left-tailed
  • B. right-tailed
  • C. two-tailed
  • D. no-tailed

Exercise 5

The p-value for this test is:

  • A. 0.0068
  • B. 0.0034
  • C. 0.0047
  • D. 0.0136

Exercise 6

At the 5% level, the correct conclusion is:

  • A. The average consumption in Santa Clara County is less than 28 pounds.
  • B. The average consumption in Santa Clara County is not 28 pounds.
  • C. The average consumption in Santa Clara County is less than 24 pounds.
  • D. The average consumption in Santa Clara County is 24 pounds.

Questions 7 and 8 refer to the following:

A hospital administrator wants to determine the proportion of emergency room patients that use the emergency room (ER) for non-emergency care. She randomly samples records from 350 ER patients and determines that 74 of those patients required only non-emergency care.

Exercise 7

The administrator constructs a 90% confidence interval for the true proportion of all ER patients who use the ER for non-emergency care. The error bound for the proportion EBP for this confidence interval is:

  • A. 0.036
  • B. 0.072
  • C. 0.030
  • D. 0.106

Exercise 8

If the same data were used but the confidence level used was 95% instead of 90%, the error bound for the proportion EBP would be:

  • A. larger
  • B. the same
  • C. smaller
  • D. we are unable to determine unless another sample is obtained

Exercise 9

What is meant by the term “95% confident” when constructing a confidence interval for a mean?

  • A. If we took repeated samples, approximately 95% of the samples would produce the same confidence interval.
  • B. If we took repeated samples, approximately 95% of the confidence intervals calculated from those samples would contain the sample mean.
  • C. If we took repeated samples, the sample mean would equal the population mean in approximately 95% of the samples.
  • D. If we took repeated samples, approximately 95% of the confidence intervals calculated from those samples would contain the true value of the population mean.

Questions 10 through 11 refer to the following:

An aircraft manufacturer is testing a new procedure to be used in installing a certain component in an aircraft. For a random sample of 8 airplanes being assembled, the time (in minutes) required to install the component for each of these 8 aircrafts are:

80; 84; 87; 91; 91; 95; 102; 106

Assume the underlying population of installation times is approximately normally distributed.

Exercise 10

Find the 90% confidence interval for the true mean installation time using this new procedure.

  • A. (86.1, 97.9)
  • B. (86.9, 91.1)
  • C. (87.2, 96.8)
  • D. Not enough information

Exercise 11

The value that is the center of the confidence interval is:

  • A. 91
  • B. 92
  • C. 93
  • D. μ

Exercise 12

The amount of soda contained in a can for a certain brand of soda is normally distributed with a population standard deviation of 0.1 ounces. A random sample of 40 cans of soda was selected and the amount of soda in each can was measured. The sample mean was 12.03 ounces and the sample standard deviation was 0.08 ounces.

What is the appropriate distribution to use when calculating a confidence interval for the true mean amount of soda contained in all cans of this brand?

  • A. The student-t distribution, because the sample standard deviation is given.
  • B. The student-t distribution, because the repair costs are approximately normally distributed.
  • C. The standard normal distribution, because the population standard deviation is known.
  • D. The standard normal distribution, because the sample mean is known.

Questions 13 – 15 refer to the following:

Two competing parcel-delivery firms in a large city make conflicting claims about which one delivers parcels in the shortest time. A random sample of 100 delivery times for the first company produces a sample mean of x1 = 37 minutes and a sample standard deviation of s1 = 10 minutes. A random sample of 100 delivery times for the second company produces a sample mean of x2 = 41 minutes and a sample standard deviation of s2 = 12 minutes. Conduct a hypothesis test to determine if the mean delivery time for the first company is less than that for the second company.

Exercise 13

What is the appropriate distribution to use when calculating a confidence interval for the true mean amount of soda contained in all cans of this brand?

  • A. m1 < m2
  • B. m1 > m2
  • C. m1 £ m2
  • D. m1 ³ m2

Exercise 14

The exact distribution for the hypothesis test is:

  • A. The normal distribution because the population standard deviations are given.
  • B. The student-t distribution because the population standard deviations are unknown.
  • C. The exponential distribution because the time of delivery decreases.
  • D. Not able to determine.

Exercise 15

f the p-value is 0.0056, the conclusion is:

  • A. The mean delivery time for the first company is higher than the mean delivery time for the second company.
  • B. The mean delivery time for the first company is no more than the mean delivery time for the second company.
  • C. The mean delivery time for the first company is at least equal to the mean delivery time for the second company.
  • D. The mean delivery time for the first company is less than the mean delivery time for the second company.

Questions 16 – 17 refer to the following:

Participants in a random sample of 10 professional football players are placed on a yogurt-and-banana diet for one month. The weights before and after one month on the diet are as follow:

Table 1
Before 187 205 165 193 199 286 212 189 242 253
After 175 193 167 190 197 240 210 189 221 255

We want to determine if the yogurt-and-banana diet helps reduce the weight of the football players. Assume the weight of the professional football players is approximately normally distributed.

Exercise 16

This is a test of:

  • A. Two independent population means, population standard deviations known.
  • B. Two independent population means, population standard deviations unknown.
  • C. Paired or matched samples.
  • D. Two population proportions.

Exercise 17

The distribution for the hypothesis test is:

  • A. Student-t
  • B. Exponential
  • C. Normal
  • D. Uniform

Exercise 18

A newspaper/TV network survey was conducted to determine whether the percentage of adult males who favor the death penalty is greater than the percentage of adult females who favor the death penalty. A random sample of 800 adult males produced 480 who favor the death penalty., while a random sample of 800 adult females produced 410 who favor the death penalty.

The Type I error is to:

  • A. Conclude that the percentage of adult males who favor the death penalty is greater than the percentage of adult females who favor the death penalty when, in fact, the percentage of males is no more than the percentage of females.
  • B. Conclude that the percentage of adult males who favor the death penalty is no more than the percentage of adult females who favor the death penalty when, in fact, the percentage of males is more than the percentage of females.
  • C. Conclude that the percentage of adult males who favor the death penalty is greater than the percentage of adult females who favor the death penalty when, in fact, the percentage of males is actually greater than the percentage of females.
  • D. Conclude that the percentage of adult males who favor the death penalty is no more than the percentage of adult females who favor the death penalty when, in fact, the percentage of males is actually no more than the percentage of females.

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