STAT 121 Practice Exam

75. What does significant in the statistical sense mean?

d) not likely to happen just by chance if H0 were true.

54. Level of confidence can be defined as

d) the percentage of the time that the procedure will produce intervals that contains the parameter value.

2. Which one of the following is NOT a parameter?

d) the proportion in a sample survey that favor a certain opinion.

1. What is the random variable of the sampling distribution of x̄?

d) the sample mean

26. What is the difference between σ and s?

b) σ is the standard deviation of a population whereas s is the standard deviation of a sample.

73. Suppose you are testing H0 : μ = 30 vs. Ha : μ > 30 with a sample of size n = 19 and the test statistic is t = 1.92. What is the P-value?

c) 0.025 < P-value < 0.05

10. Referring to the sampling distribution of x̄ described in the previous question, what is the standard deviation of the sampling distribution of x̄?

c) 1.0

14. Referring to the manufacturing process in question 12 above, what are the lower and upper limits for the control chart for x̄ from samples of size 16?

c) 14.8, 15.2

57. The manager of a major chain department store decided to offer a promotion to increase customers' usage of their credit cards issued by the chain. Before the promotion, credit card holders used their cards an average of 6.3 times per month. During the month of the promotion a random sample of 100 credit card holders used their cards an average of 6.8 times with a standard deviation of 2.5. For testing the hypotheses H0 : μ = 6.3 versus Ha : μ > 6.3, what is the value of the standardized test statistic?

c) 2.00

68. A poultry farmer wishes to estimate the average incubation period (the number of days between a hen laying her egg and the time the egg hatches) for eggs on his farm. He plans to take a sample and make a 98% confidence interval, and would like a margin of error of half a day. It is known that the distribution of incubation lengths has a standard deviation of 1.5 days. How many eggs does he need to sample to create the desired interval?

c) 49

71. Which one of the following is NOT a correct statement about margin of error?

c) For fixed sample size, decreasing level of confidence increases the margin of error.

50. A quality control engineer needs to determine whether the oven temperature for a certain model is properly calibrated on average. Ten ovens are set at 300o F, and after one hour, the actual temperature will be measured. What hypotheses should be used to test whether the average temperature differs from 300o F?

c) H0 : μ = 300 versus Ha: μ ≠ 300

63. What do we obtain from the sampling distribution of x̄, created assuming the null hypothesis is true, in order to perform a test of hypothesis?

c) P-value.

11. For the sampling distribution of x̄ described in question 9, what is its shape?

c) Slightly left skewed

49. Refer to the above question. Suppose x̄ = 50.15 bushels per acre. Graphically, what represents the P-value?

c) The area under the sampling distribution of x̄ curve to the right of 50.15

44. Referring to question 43, the mean of the sample is 173 mg and the margin of error for the confidence interval given in the above question is 21 mg. Which one of the following is a correct interpretation of margin of error?

c) The maximum difference we expect between our sample result and the true average weekly oral dose is no more than 21 mg.

8. A random sample of size 10 was taken from a population. The sample has a standard deviation of zero. Which of the following statements must be true.

c) The ten data points in the sample are all equal in numerical value.

39. Suppose you are testing the following hypotheses. What is the type I error for these hypotheses? H0 : Cake is not done, versus Ha : Cake is done

c) To believe that the cake is done when it is still not done.

9. For the theoretical sampling distribution of x̄ created by taking all possible samples of size 16 from a very left skewed population with μ = 22 and σ = 4, the mean of this sampling distribution

c) is exactly equal to 22.

74. The null hypothesis is a statement of

c) no effect or no change in the population parameter.

38. When using a confidence interval to perform a two-sided test, H0 will be rejected whenever

c) the claimed parameter value in H0 falls outside the confidence interval.

67. What is the purpose of a confidence interval?

c) to estimate the value of a parameter

27. The time it takes college freshman to complete the Mason Basic Reasoning Test is normally distributed with a mean of 24 minutes and a standard deviation of 5 minutes. What symbol should be used to represent the mean of 24 minutes?

c) μ

64. Which of the following is NOT one of the conditions for using the formula x̄ ± t ?

c) σ, the standard deviation of the population, must be known

60. Which one of the following does NOT affect margin of error for a one-sample t confidence interval for μ? (Assume that the necessary conditions are met.)

d) Value of the parameter μ.

33. Find a 95% confidence interval for µ when n = 9, x̄ = 103.14 and s = 5.25.

a) (99.10, 107.18)

25. Fill in the blank: For the sampling distribution of x̄ created by taking random samples from a left skewed population, the standard deviation of the sampling distribution of x̄ ____________ as n increases.

a) Decreases

47. The mean weight for starting football players on a top 20 team in Division I was 105 kg in the 1988 football season. The question asked by a researcher was whether starters on non-top 20 teams weighed less than 105 kg on the average. Thirty six starting players on non-top 20 teams were randomly selected. What are the null and alternative hypotheses necessary to answer the question, "Is the mean weight for non-top 20 starters less than 105 kg?"

a) H0 : μ = 105 versus Ha: μ < 105

56. Suppose we have H0 : μ = 30 versus Ha : μ > 30 with P-value = .032. If we decided to test H0 : μ = 30 versus Ha : μ ≠ 30, what is the P-value for this new Ha assuming all other factors are the same?

d) .064

34. Suppose we were to test the hypotheses H0 : µ = 80 versus Ha : µ < 80 and computed the standardized value of the test statistic to be t = -2.67 from the sample results of a sample of size n = 22. Using the t table, what is the P-value?

d) 0.005 < P < 0.01

70. Calculate the margin of error from a random sample of 27 pigs with a mean weight of 54.3 kg and a standard deviation s = 6.2 kg. Use 95% confidence.

d) 2.45 kg.

16. On a control chart, under what circumstance is the process out of control?

d) All of the above

48. We want to test the hypotheses H0 : μ = 50 versus Ha : μ > 50 to determine whether a new variety of corn will yield more than 50 bushels per acre. We plan to sample 100 plots and measure yield per acre on each plot. Assuming H0 is true and that σ = 5, describe the sampling distribution of x̄.

d) Approximately normal with mean 50 and standard deviation 0.5.

59. Which one of the following is a correct interpretation of the P-value given above in question 63?

d) The probability of obtaining a sample mean that is as far or farther from the hypothesized mean value of 6.3 as the observed value of 6.8 is .013.

6. The theoretical sampling distribution of a statistic consists of

b) the values of a statistic from all possible samples.

7. The standard deviation of the sampling distribution of x̄ measures

b) the variability of the sample mean values about the parameter, μ.

29. We use a t-distribution with n-1 degrees of freedom rather than the standard normal distribution whenever

b) we are using s to estimate σ

62. Which one of the following is NOT synonymous with "Reject H0"?

d) The results are due to chance.

42. The purpose of a confidence interval is to provide

d) a range of plausible values that a parameter could take.

4. The sampling distribution of a statistic has the following:

d) all of the above.

69. The radius of a wheel on a toy car is supposed to be 3/4 of an inch. If the wheel is too small or too large, the car will not roll properly. The manufacturer measures the radius in a random sample of 20 cars to determine whether the mean radius of the wheels currently being produced is different from 3/4 of an inch. Select the correct null and alternative hypotheses for this test.

a) H0 : μ = 3/4 in. versus Ha: μ ≠ 3/4 in.

61. Which one of the following is NOT part of the definition for P-value?

a) Probability that the null hypothesis is true.

58. Suppose the P-value for the test described in the above question is 0.013 (although this is not the correct value.) What is the appropriate statistical conclusion at the .05 level of significance?

a) Reject H0 and conclude that the mean exceeds 6.3 times per month

55. Which hypothesis is assumed to be true until evidence is found to disprove or contradict it?

a) The null hypothesis.

41. In 1990, the average cost of a normal pregnancy and delivery was $4334. Data was collected recently on a random sample of 39 recent births in a particular state. A 90% confidence interval was computed to be ($4663, $4787). On the basis of this interval, can we say that the average cost in that particular state is different from the average cost of $4334? Why or why not?

a) Yes, because $4,334 is outside the confidence interval. b) Yes, because the mean for the sample of 39 births is $4,7

22. Lifetimes of a particular flashlight battery have a non-Normal distribution with mean, µ, of 35.6 hours and standard deviation σ = 5.4 hours. A quality inspector is planning to take a random sample of 43 of these batteries and compute the sample mean. Can he compute the probability that the sample mean will be below 35.7 hours using the standard Normal table? Why or why not?

a) Yes, because the sample will be large and random so the Central Limit Theorem applies.

20. The standard deviation of the sampling distribution of x̄ is _____________ the standard deviation of the population from which samples of size n >1 are taken to create the sampling distribution.

a) less than

32. Whenever performing a one sample t procedure on means, we should check for

a) randomization and no outliers in the data.

72. Fill in the blank: Keeping all else constant, the sample mean of thirty measurements will have a margin of error that is..........the margin of error for a sample mean of three measurements.

a) smaller than

18. Control charts are designed to sound an alarm when

a) the amount of observed variation exceeds the amount that could be attributable to natural variation.

36. Sample results are said to be statistically significant whenever

a) the difference between the observed statistic and the claimed parameter value given in H0 is too large to be due to chance.

28. Fill in the blank: The t-distribution with 8 degrees of freedom has ____________________ the standard Normal distribution.

a) the same center but is more spread out than

3. Fill in the blank: Central Limit Theorem allows us to compute probabilities on ___________ using the standard Normal table provided the sample size of the random sample is sufficiently large.

a) x̄

17. Which one of the following is not a statistic?

a) μ

23. Referring to the above question and assuming that computing the probability is okay, what is the probability that the sample mean is below 35.7?

b) 0.5478

45. Suppose we are testing the hypotheses H0 : μ = 850 versus the hypothesis Ha : μ > 850. For α = 0.05 and P-value = .092, what decision should be made?

b) Fail to reject Ho

46. What two things do we need in order to compute margin of error for a one-sample t confidence interval for μ?

b) Level of confidence and the standard error of x̄.

13. Do you need to apply the Central Limit Theorem to compute the probability on the mean weight of 16 randomly selected bags described in the above question?

b) No, because the distribution of weights is Normally distributed.

52. How is level of confidence determined?

b) Subjectively determined by the researcher.

53. Which hypothesis does the researcher generally want to prove?

b) The alternative hypothesis.

43. The weekly oral dosage of anabolic steroids was measured on a sample of 20 body builders. A 95% confidence interval estimate for the average weekly oral dose of anabolic steroids obtained from these results was 152 mg to 194 mg. Which one of the following is a correct interpretation of this confidence interval?

b) We are 95% confident that the average weekly dose of anabolic steroids used by all body builders is between 152 mg. and 194 mg.

35. If we fail to reject the null hypothesis, we could be making

b) a type II error.

24. Fill in the blank: For the sampling distribution of x̄ created by taking random samples from a left skewed population, the shape is _______________ for large n.

b) approximately Normal

40. The margin of error in a confidence interval covers only which kind of errors?

b) chance errors due to random sampling

30. Standard error of x̄ refers to

b) the estimate of the standard deviation of the sampling distribution of x̄.

66. A test of significance is intended to assess

b) the evidence provided by data against the null hypothesis in favor of the alternative hypothesis.

65. Margin of error for 99% confidence tells us

b) the most a statistic differs from the parameter for the middle 99% of all possible statistic values.

19. The Central Limit Theorem says that

b) the sampling distribution of x̄ is approximately Normal when the sample size is large.

5. Which one of the following measures the variability of a statistic?

b) the standard deviation of the sampling distribution for the statistic.

12. A manufacturing process produces potato chip bags that have Normally distributed weights, with a mean weight of 15 oz. and a standard deviation of .3 oz. What is the probability that 16 randomly selected bags have a mean weight that exceeds 15.2 oz?

e) 0.0038

21. The mean score of the fourth exam in a statistics class with 1800 students at a large university was 79 with a standard deviation of 14. Suppose twenty-five students are to be randomly selected and their sample mean computed. What will be the mean and standard deviation of the sampling distribution of x̄?

e) 79.0, 2.8

51. Statistically significant is equivalent to all of the following except one. Which one is not equivalent?

e) The difference between an observed statistic and the true parameter value is due to chance variation

15. The Central Limit Theorem tells us that under certain conditions

e) the shape of the sampling distribution of x̄ will be approximately Normal.