1. The absolute value of the difference between the point estimate and the population parameter it estimates is

- the standard error
- the sampling error
- precision
- the error of confidence

2. A population has a standard deviation of 50. A random sample of 100 items from this population is selected. The sample mean is determined to be 600. At 95% confidence, the margin of error is

- 5
- 9.8
- 650
- 609.8

3. As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution

- becomes larger
- becomes smaller
- stays the same
- None of these alternatives is correct.

4. Using an α = 0.04 a confidence interval for a population proportion is determined to be 0.65 to 0.75. If the level of significance is decreased, the interval for the population proportion

- becomes narrower
- becomes wider
- does not change
- remains the same

5. It is known that the variance of a population equals 1,936. A random sample of 121 has been taken from the population. We can be 95% confident that the sample mean will provide a margin of error of

- 7.84
- 31.36
- 344.96
- 1,936

6. A random sample of 144 observations has a mean of 20, a median of 21, and a mode of 22. The population standard deviation is known to equal 4.8. The 95.44% confidence interval for the population mean is

- 15.2 to 24.8
- 19.200 to 20.800
- 19.216 to 20.784
- 21.2 to 22.8

7. It is known that the population variance equals 484. With a 0.95 probability, the sample size that needs to be taken if the desired margin of error is 5 or less is

- 25
- 74
- 189
- 75

8. The following random sample from a population whose values were normally distributed was collected. 10 8 11 11 The 95% confidence interval for μ is

- 8.52 to 10.98
- 7.75 to 12.25
- 9.75 to 10.75
- 8.00 to 10.00

9. Which of the following best describes the form of the sampling distribution of the sample proportion?

- When standardized, it is exactly the standard normal distribution.
- When standardized, it is the t distribution.
- It is approximately normal as long as n ≥ 30.
- It is approximately normal as long as np ≥ 5 and n(1-p) ≥ 5.

10. A random sample of 1000 people was taken. Four hundred fifty of the people in the sample favored Candidate A. The 95% confidence interval for the true proportion of people who favors Candidate A is

- 0.419 to 0.481
- 0.40 to 0.50
- 0.45 to 0.55
- 1.645 to 1.96

11. We are interested in conducting a study in order to determine what percentage of voters of a state would vote for the incumbent governor. What is the minimum size sample needed to estimate the population proportion with a margin of error of 0.05 or less at 95% confidence?

- 200
- 100
- 58
- 385

12. The sum of the values of α and β

- always add up to 1.0
- always add up to 0.5
- is the probability of Type II error
- None of these alternatives is correct.

13. What type of error occurs if you fail to reject H0 when, in fact, it is not true?

- Type II
- Type I
- either Type I or Type II, depending on the level of significance
- either Type I or Type II, depending on whether the test is one tail or two tail

14. In hypothesis testing,

- the smaller the Type I error, the smaller the Type II error will be
- the smaller the Type I error, the larger the Type II error will be
- Type II error will not be effected by Type I error
- the sum of Type I and Type II errors must equal to 1

15. When the p-value is used for hypothesis testing, the null hypothesis is rejected if

- p-value ≤ α
- α < p-value
- p-value ≥ α
- p-value = 1 - α

16. If a hypothesis is not rejected at the 5% level of significance, it

- will also not be rejected at the 1% level
- will always be rejected at the 1% level
- will sometimes be rejected at the 1% level
- None of these alternatives is correct.

17. In a two-tailed hypothesis test the test statistic is determined to be Z = -2.5. The p-value for this test is

- -1.25
- 0.4938
- 0.0062
- 0.0124

Use the following to answer the next 3 questions:

The average gasoline price of one of the major oil companies in Europe has been $1.25 per liter. Recently, the company has undertaken several efficiency measures in order to reduce prices. Management is interested in determining whether their efficiency measures have actually reduced prices. A random sample of 49 of their gas stations is selected and the average price is determined to be $1.20 per liter. Furthermore, assume that the standard deviation of the population is $0.14.

18. The standard error has a value of

- 0.14
- 7
- 2.5
- 0.02

19. The value of the test statistic for this hypothesis test is

- 1.96
- 1.645
- -2.5
- -1.645

20. The p-value for this problem is

- 0.4938
- 0.0062
- 0.0124
- 0.05

21. To construct an interval estimate for the difference between the means of two populations when the standard deviations of the two populations are unknown and it can be assumed the two populations have unequal variances, we must use a t distribution with (let n1 be the size of sample 1 and n2 the size of sample 2)

- (n1 + n2) degrees of freedom
- (n1 + n2 - 1) degrees of freedom
- (n1 + n2 - 2) degrees of freedom
- None of the above

22. The width of a confidence interval estimate for a proportion will be

- wider for a sample size of 100 than for a sample size of 50.
- narrower when the sample proportion is 0.50 than when the sample proportion is 0.20.
- narrower for 90% confidence than for 95% confidence.
- narrower for 99% confidence than for 95% confidence.

23. What type of car is more popular among college students, American or foreign? One hundred fifty-nine college students were randomly sampled and each was asked which type of car he or she prefers. The resulting 90% confidence interval for the proportion p of college students that prefer American cars is (0.332, 0.460). Which of the following is a correct interpretation of the interval?

- 90% of all college students prefer American cars between .332 and .460 of the time.
- We are 90% confident that the proportion p of all college students who prefer American cars falls between .332 and .460.
- We are 90% confident that the interval (0.332, 0.460) contains the true proportion p of all college students who prefer American cars.
- We are 90% confident that the sample proportion of the 159 sampled students who prefer American cars falls between .332 and .460.
- e. Between 0.332 and 0.446 of American cars are preferred by college students.

Use the following information to answer the next 2 questions:

A biologist has collected bivariate data where the independent (B) variable is the number of cricket chips per minute and the dependent (C) variable is the temperature in °F. The data can be summarized as follows: ๐=7,๐ฅฬ =17.429,๐ ๐ฅ=1.988,๐ ๐ฆ=8.696,๐=0.976 24. The slope of the least squares line is approximately

- 6.13
- 4.27
- 0.234
- 0.163
- 0.976

25. What proportion of the variation in temperature (C) is explained by the linear relationship between the number of cricket chirps (B) and temperature?

- 0.024
- 0.976
- 1.9888.696
- (.976)2
- 17.42980.571

26. A relief fund is set up to collect donations for the families affected by recent storms. A random sample of 400 people shows that 28% of those 200 who were contacted by telephone actually made contributions compared to only 18% of the 200 who received first class mail requests. Which formula calculates the 95% confidence interval for the difference in the proportions of people who make donations if contacted by telephone or first class mail?

- (0.28−0.18)±1.96√0.23×0.77200
- (0.28−0.18)±1.96√0.23×0.77200+0.23×0.77200
- (0.28−0.18)±1.96√0.23×0.77400
- (0.28−0.18)±1.96√0.28×0.72400+0.18×0.82400
- (0.28−0.18)±1.96√0.28×0.72200+0.18×0.82200

27. A sample of 41 observations yielded a sample standard deviation of 5. If we want to test H0: ๐2 = 20, the test statistic is

- 100
- 10
- 51.25
- 50

28. A sample of 20 cans of tomato juice showed a standard deviation of 0.4 ounces. A 95% confidence interval estimate of the variance for the population is

- 0.2313 to 0.8533
- 0.2224 to 0.7924
- 0.3042 to 0.5843
- 0.0925 to 0.3413

29. A Regression analysis between sales (Y in $1000) and advertising (X in dollars) resulted in the following equation ลท = 30,000 + 4X The above equation implies that an

- increase of $4 in advertising is associated with an increase of $4,000 in sales
- increase of $1 in advertising is associated with an increase of $4 in sales
- increase of $1 in advertising is associated with an increase of $34,000 in sales
- increase of $1 in advertising is associated with an increase of $4,000 in sales

30. If the coefficient of determination is equal to 1, then the coefficient of correlation

- must also be equal to 1
- can be either -1 or +1
- can be any value between -1 to +1
- must be -1

31. If the coefficient of correlation is -0.4, then the slope of the regression line

- must also be -0.4
- can be either negative or positive
- must be negative
- must be 0.16

Use the following information to answer the next 3 questions:

You are given the following information about y and x.

y

12

3

7

6

x

4

6

2

4

32. The least squares estimate of b1 equals

- 1
- -1
- -11
- 11

e. None of the above

33. The least squares estimate of b0 equals

- 1
- -1
- -11
- 11

e. None of the above

34. The coefficient of determination equals

- -0.4364
- 0.4364
- -0.1905
- 0.1905

35. For a given level of significance (α), if the sample size n is increased, the probability of a Type II error (β)

- will remain the same.
- will decrease.
- will increase.
- cannot be determined

36. If the p value is less than a in a two-tailed test,

- the null hypothesis should be rejected.
- the null hypothesis should not be rejected.
- a one-tailed test should be used.
- no conclusion should be reached.

37. For a random sample of several hundred executives holding MBA degrees, the 0.95 confidence interval estimate of their mean salary is $32,160 to $37,840. If, for the same sample, the level of confidence is increased, how will the length of the confidence interval estimate change?

- It will decrease,
- It will remain the same.
- It will increase.
- The effect cannot be determined from the information given.

38. Weights of boxes filled with oranges from a certain grove are normally distributed. A random sample of nine boxes has a mean of 42.7 lbs and a standard deviation of 2.1 lbs. What is the 0.90 confidence interval estimate of the mean weight of all boxes from this grove?

- The sample is too small to make an estimate,
- 42.7 ± 1.86(0.7)
- 42.7 ± 1.40(0.7)
- 42.7 ± 1.65 (0.7)

39. The hypothesis Ho: μ = 100 is to be tested with α = 0.05 against the alternative H1: μ > 100. A sample of n = 25 yields ๐ฅฬ = 105, s = 15. The correct decision is:

- Do not reject the null hypothesis because 1.67 < 1.708.
- Reject the null hypothesis because 1.67 > 1.645.
- Do not reject null hypothesis because 1.67 < 1.711
- Do not reject the null hypothesis because 1.67 < 2.064.

40. For a sample of size 20 taken from a normally distributed population with standard deviation equal to 5, a 90% confidence interval for the population mean would require the use of

- t = 1.328
- t = 1.729
- z = 1.96
- z = 1.645

41. Suppose that the brilliance of a certain type of lightbulb is normally distributed with a known standard deviation of 50 lumens. What size sample should we select if we want to have 95 percent confidence that the sample mean is within 24 lumens of the population mean?

- 17
- 16
- 15
- 12 42.

It is desired to find the 0.95 confidence interval estimate for the proportion of voters who prefer candidate A in the New Hampshire primary. On the basis of 1600 voters selected at random, 320 prefer candidate A. The 0.95 confidence interval for the proportion is: a. 320 ± 1 .96(0.0 l) b. 0.2 ± 1.645(1.0l) c. 0.2 ± 1.96(0.01) d. 0.8 ± l .96(0.01)

43. A hypothesis test is used to prevent a machine from under filling or overfilling quart-bottles of beer. On the basis of a sample, the hypothesis is rejected and the machine is shut down for inspection. A thorough examination reveals there is nothing wrong with the filling machine. From a statistical point of view:

- A correct decision was made,
- A type I and type II error were made,
- A type I error was made,
- A type II error was made.

44. A two-tailed test for the population mean is to be performed at the 0.01 level of significance. The population is normally distributed with unknown standard deviation. Twelve observations are to be used in the test. Which of the following is the absolute value of the table value, to 3 decimals, that should be used in the test?

- 2.681
- 2.718
- 3.055
- 3.106 45.

A random sample of 400 voters has been selected to test the null hypothesis that at least 50 percent are Democrats. The alternative hypothesis is that less than 50% are democrats. The level of significance is 0.05. What is the critical proportion of Democrats for the sample that, if not exceeded, will cause rejection of the null hypothesis?

- 0.54
- 0.45
- 0.55
- 0.46

46. A type II error is committed

- When we reject a true null hypothesis
- When we do not reject a false null hypothesis
- When we do not reject a false alternative hypothesis
- When we do not reject a true null hypothesis

47. Two normally distributed populations have standard deviations of 6 inches. A two-sided test of the hypothesis that the populations have equal means is to be conducted. The sample size will be 15 for one population and 10 for the other. What is the standard error of the difference in means?

- 1.20 inches
- 2.45 inches
- 1.00 inches
- 6.0 inches

48. Two populations are normally distributed with equal but unknown variances. A sample of 12 will be selected from one of the populations and a sample of 9 will be selected from the other. What statistic should be used in a test of the hypothesis that the two population means are equal?

- z
- t with 21 degrees of freedom
- d with 19 degrees of freedom
- t with 19 degrees of freedom

49. If the calculate z-value for a test statistic on a one-tail test equals 2.45, what is the P-value?

- 0.7600
- 0.0036
- 0.0142
- 0.0071

50. A random sample of size 20 taken from a normally distributed population resulted in a sample variance of 32. The lower limit of a 90% confidence interval for the population variance would be:

- 52.185
- 20.375
- 20.170
- 54.931

51. A marketing research director believes that a new package increase sales. Twelve pairs of stores, matched on socioeconomic characteristics in their market areas, are chosen to test the hypothesis: H0: μD = 0 H1: μD > 0 lf 0.1 is the significance level, what critical value should be used in this test?

- 1.65
- 1.96
- 1.363
- 1.356

52. Which of the following statements is not true about the level of significance in a hypothesis test?

- The larger the level of significance, the more likely you are to reject the null hypothesis.
- The level of significance is the maximum risk we are willing to accept in making a Type I error.
- The significance level is also called the α level.
- The significance level is another name for Type II error.

53. In constructing a 90% interval estimate for the ratio of two population variances, ๐1 2/๐2 2, two independent samples of sizes 40 and 60 are drawn from the populations. If the sample variances are 515 and 920, then the lower confidence limit is:

- 0.352
- 0.341
- 0.890
- 0.918

54. In a hypothesis test for the population variance, the hypotheses are H0 : σ2 = 30 vs. H0 : σ2 < 30 If the sample size is 20 and the test is being carried out at the 5% level of significance, the null hypothesis will be rejected if:

- ๐2 < 30.144
- ๐2 > 10.851
- ๐2 < 10.117
- ๐2 > 31.410 55.

When the necessary conditions are met, a two-tail test is being conducted to test the difference between two population proportions. The two sample proportions are 1 pˆ ๏ฝ 0.20 and 2 pˆ ๏ฝ 0.15 , and the standard error of the sampling distribution of 1 2 pˆ ๏ญ pˆ is 0.25. The calculated value of the test statistic will be:

- z = 0.2
- z = 1.15
- t = 2.0
- t = 1.2

56. Two independent samples of sizes 35 and 40 are randomly selected from two normally distributed populations. Assume that the population variances are unknown but equal. In order to test the difference between the population means, 1 2 ๏ญ ๏ญ๏ญ , the sampling distribution of the sample mean difference, 1 2 x ๏ญ x , is:

- normally distributed
- t-distributed with 75 degrees of freedom
- t-distributed with 73 degrees of freedom
- F-distributed with 34 and 39 degrees of freedom

57. The number of degrees of freedom associated with the t-test, when the data are gathered from a matched pairs experiment with 15 pairs, is:

- 30
- 15
- 28
- 14

58. After calculating the sample size needed to estimate a population proportion to within 0.05, you have been told that the maximum allowable error must be reduced to just 0.025. If the original calculation led to a sample size of 1000, the sample size will now have to be:

- 2000
- 4000
- 1000
- 8000

59. A sample of size 200 from population 1 has 50 successes. A sample of size 200 from population 2 has 40 successes. The value of the test statistic for testing the null hypothesis that the proportion of successes in population 1 exceeds the proportion of successes in population 2 by 0.025 is:

- 1.96
- 1.25
- 0.5998
- 1.20

60. In constructing 90% confidence interval estimate for the difference between the means of two normally distributed populations, where the unknown population variances are assumed not to be equal, summary statistics computed from two independent samples are as follows: 40 1 n ๏ฝ , 95 1 x ๏ฝ , 12.5 1 s ๏ฝ , 30 2 n ๏ฝ , 75 2 x ๏ฝ , and 35.5 2 s ๏ฝ . The lower confidence limit is:

- 30.086
- 8.542
- 0.914
- 31.458