ECO 2200 Unit 2
The process that produces Sonora Bars (a type of candy) is intended to produce bars with a mean weight of 56 gm. The process standard deviation is known to be 0.77 gm. A random sample of 49 candy bars yields a mean weight of 55.82 gm. Find the test statistic to see whether the candy bars are smaller than they are supposed to be. A. -1.636 B. -1.645 C. -1.677
-1.636
Dullco Manufacturing claims that its alkaline batteries last at least 40 hours on average in a certain type of portable CD player. But tests on a random sample of 18 batteries from a day's large production run showed a mean battery life of 37.8 hours with a standard deviation of 5.4 hours. To test DullCo's hypothesis, the test statistic is: A. -1.980 B. -1.728 C. -2.101 D. -1.960
-1.728
In a left-tailed test comparing two means with variances unknown but assumed to be equal, the sample sizes were n1 = 8 and n2 = 12. At α = .05, the critical value would be: A. -1.960 B. -2.101 C. -1.734 D. -1.645
-1.734
In the nation of Gondor, the EPA requires that half the new cars sold will meet a certain particulate emission standard a year later. A sample of 64 one-year-old cars revealed that only 24 met the particulate emission standard. The test statistic to see whether the proportion is below the requirement is: A. -1.645 B. -2.066 C. -2.000 D. -1.960
-2.000
When testing the hypothesis H0: μ = 100 with n = 100 and σ2 = 100, we find that the sample mean is 97. The test statistic is: A. -3.000 B. -10.00 C. -0.300 D. -0.030
-3.000
Last year, 10 percent of all teenagers purchased a new iPhone. This year, a sample of 260 randomly chosen teenagers showed that 39 had purchased a new iPhone. To test whether the percentage has risen, the critical value at α = .05 is: A. 1.645 B. 1.658 C. 1.697 D. 1.960
1.645
Guidelines for the Jolly Blue Giant Health Insurance Company say that the average hospitalization for a triple hernia operation should not exceed 30 hours. A diligent auditor studied records of 16 randomly chosen triple hernia operations at Hackmore Hospital and found a mean hospital stay of 40 hours with a standard deviation of 20 hours. "Aha!" she cried, "the average stay exceeds the guideline." The value of the test statistic for her hypothesis is: A. 2.080 B. 0.481 C. 1.866 D. 2.000
2.000
Guidelines for the Jolly Blue Giant Health Insurance Company say that the average hospitalization for a triple hernia operation should not exceed 30 hours. A diligent auditor studied records of 16 randomly chosen triple hernia operations at Hackmore Hospital and found a mean hospital stay of 40 hours with a standard deviation of 20 hours. "Aha!" she cried, "the average stay exceeds the guideline." At α = .025, the critical value for a right-tailed test of her hypothesis is: A. 1.753 B. 2.131 C. 1.645 D. 1.960
2.131
A sample of 16 ATM transactions shows a mean transaction time of 67 seconds with a standard deviation of 12 seconds. Find the test statistic to decide whether the mean transaction time exceeds 60 seconds. A. 1.457 B. 2.037 C. 2.333 D. 1.848
2.333
A sample of 16 ATM transactions shows a mean transaction time of 67 seconds with a standard deviation of 12 seconds. Find the critical value to test whether the mean transaction time exceeds 60 seconds at α = .01. A. 2.947 B. 2.602 C. 2.583 D. 2.333
2.602
Last year, 10 percent of all teenagers purchased a new iPhone. This year, a sample of 260 randomly chosen teenagers showed that 39 had purchased a new iPhone. The test statistic to find out whether the percentage has risen would be: A. 2.687 B. 2.758 C. .0256 D. 2.258
2.687
For a sample size of n = 100, and σ = 10, we want to test the hypothesis H0: μ = 100. The sample mean is 103. The test statistic is: A. 1.645 B. 1.960 C. 3.000 D. 0.300
3.000
Does the Speedo Fastskin II Male Hi-Neck Bodyskin competition racing swimsuit improve a swimmer's 200-yard individual medley performance times? A test of 100 randomly chosen male varsity swimmers at several different universities showed that 66 enjoyed improved times, compared with only 54 of 100 female varsity swimmers. To test for equality in the proportions of men versus women who experienced improvement, the test statistic is approximately: A. 1.73 B. 1.47 C. 2.31 D. Can't tell without knowing the tail of the test
A. 1.73
Carver Memorial Hospital's surgeons have a new procedure that they think will decrease the time to perform an appendectomy. A sample of 8 appendectomies using the old method had a mean of 38 minutes with a variance of 36 minutes, while a sample of 10 appendectomies using the experimental method had a mean of 29 minutes with a variance of 16 minutes. For a right-tailed test of means (assume equal variances), the test statistic is: A. 3.814 B. 2.365 C. 3.000 D. 1.895
A. 3.814
Which test should we use to test for zero difference in mean times? A. Paired t-test B. Independent samples t-test C. Independent samples z test D. Cannot be sure without knowing α.
A. Paired t-test
The F-test for equality of variances assumes: A. normal populations. B. equal means. C. equal sample sizes. D. equal means and sample sizes.
A. normal populations.
In a test for equality of two proportions, the sample proportions were p1 = 12/50 and p2 = 18/50. The test statistic is approximately: A. -1.44. B. -1.31 C. -1.67. D. Must know α to answer
B. -1.31
In a random sample of patient records in Cutter Memorial Hospital, six-month postoperative exams were given in 90 out of 200 prostatectomy patients, while in Paymor Hospital such exams were given in 110 out of 200 cases. In a left-tailed test for equality of proportions, the test statistic is: A. -1.96 B. -2.00 C. -4.00 D. -3.48
B. -2.00
In a right-tailed test comparing two means with known variances, the sample sizes were n1 = 8 and n2 = 12. At α = .05, the critical value would be: A. 1.960 B. 1.645 C. 1.734 D. 1.282
B. 1.645
A random sample of Ersatz University students revealed that 16 females had a mean of $22.30 in their wallets with a standard deviation of $3.20, while 16 males had a mean of $17.30 with a standard deviation of $9.60. In comparing the population variances at α = .10 in a two-tailed test, we conclude that: A. the variances are equal. B. the variances are unequal. C. the variances are incomparable (different sample sizes)
B. the variances are unequal.
A random sample of Ersatz University students revealed that 16 females had a mean of $22.30 in their wallets with a standard deviation of $3.20, while 16 males had a mean of $17.30 with a standard deviation of $9.60. In comparing the population variances at α = .10 in a two-tailed test, we conclude that: A. the variances are equal. B. the variances are unequal. C. the variances are incomparable (different sample sizes).
B. the variances are unequal.
A random sample of Ersatz University students revealed that 16 females had a mean of $22.30 in their wallets with a standard deviation of $3.20, while 6 males had a mean of $17.30 with a standard deviation of $9.60. At α = .10, to test for equal variances in a two-tailed test, the critical values are: A. 0.441 and 3.24 B. 0.556 and 2.27 C. 0.345 and 4.62 D. 0.387 and 2.90
C. 0.345 and 4.62
During a test period, an experimental group of 10 vehicles using an 85 percent ethanol-gasoline mixture showed mean CO2 emissions of 667 pounds per 1000 miles, with a standard deviation of 20 pounds. A control group of 14 vehicles using regular gasoline showed mean CO2 emissions of 679 pounds per 1000 miles with a standard deviation of 15 pounds. At α = 0.05, in a left-tailed test (assuming equal variances) the test statistic is: A. -1.310 B. -2.042 C. -1.645 D. -1.683
D. -1.683
In a test for equality of two proportions, the sample proportions were p1 = 12/50 and p2 = 18/50. The pooled proportion is: A. .20 B. .24 C. .36 D. .30
D. .30
Based on a random sample of 13 tire changes, the mean time to change a tire on a Boeing 777 has a mean of 59.5 minutes with a standard deviation of 8.4 minutes. For 10 tire changes on a Boeing 787, the mean time was 64.3 minutes with a standard deviation of 12.4 minutes. To test for equal variances in a two-tailed test at α = .10, the critical values are: A. 3.73 and 0.228 B. 2.51 and 3.67 C. 3.07 and 0.398 D. 3.07 and 0.357
D. 3.07 and 0.357
For a given sample size, when we increase the probability of a Type I error, the probability of a Type II error: A. remains unchanged. B. increases. C. decreases. D. is impossible to determine without more information
Decreases
For a test of a mean, which of the following is incorrect? A. H0 is rejected when the calculated p-value is less than the critical value of the test statistic. B. In a right-tailed test, we reject H0 when the test statistic exceeds the critical value. C. The critical value is based on the researcher's chosen level of significance. D. If H0: μ ≤ 100 and H1: μ > 100, then the test is right-tailed.
H0 is rejected when the calculated p-value is less than the critical value of the test statistic.
Which of the following is not a valid null hypothesis? A. H0: μ ≥ 0 B. H0: μ ≤ 0 C. H0: μ ≠ 0 D. H0: μ = 0
H0: μ ≠ 0
A sample of 16 ATM transactions shows a mean transaction time of 67 seconds with a standard deviation of 12 seconds. State the hypotheses to test whether the mean transaction time exceeds 60 seconds. A. H0: μ ≤ 60, H1: μ > 60 B. H0: μ ≥ 60, H1: μ < 60 C. H0: μ = 60, H1: μ ≠ 60 D. H0: μ < 60, H1: μ ≥ 60
H0: μ ≤ 60, H1: μ > 60
The process that produces Sonora Bars (a type of candy) is intended to produce bars with a mean weight of 56 gm. The process standard deviation is known to be 0.77 gm. A random sample of 49 candy bars yields a mean weight of 55.82 gm. Which are the hypotheses to test whether the mean is smaller than it is supposed to be? A. H0: μ ≤ 56, H1: μ > 56 B. H0: μ ≥ 56, H1: μ < 56 C. H0: μ = 56, H1: μ ≠ 56 D. H0: μ < 56, H1: μ ≥ 56
H0: μ ≥ 56, H1: μ < 56
Which statement about α is not correct? A. It is the probability of committing a Type I error. B. It is the test's significance level. C. It is the probability of rejecting a true H0. D. It is equal to 1 - β.
It is equal to 1 - β.
John rejected his null hypothesis in a right-tailed test for a mean at α = .025 because his critical t value was 2.000 and his calculated t value was 2.345. We can be sure that: A. John did not commit a Type I error. B. John did not commit a Type II error. C. John committed neither a Type I nor Type II error. D. John committed both a Type I and a Type II error.
John did not commit a Type II error.
3. After testing a hypothesis, we decided to reject the null hypothesis. Thus, we are exposed to: A. Type I error. B. Type II error. C. Either Type I or Type II error. D. Neither Type I nor Type II error.
Type 1 error
2. After testing a hypothesis regarding the mean, we decided not to reject H0. Thus, we are exposed to: A. Type I error. B. Type II error. C. Either Type I or Type II error. D. Neither Type I nor Type II error
Type II error
Dullco Manufacturing claims that its alkaline batteries last at least 40 hours on average in a certain type of portable CD player. But tests on a random sample of 18 batteries from a day's large production run showed a mean battery life of 37.8 hours with a standard deviation of 5.4 hours. In a left-tailed test at α = .05, which is the most accurate statement? A. We would strongly reject the claim. B. We would clearly fail to reject the claim. C. We would face a rather close decision. D. We would switch to α = .01 for a more powerful test
We would face a rather close decision.
Which of the following is correct? A. When sample size increases, both α and β may decrease. B. Type II error can only occur when you reject H0. C. Type I error can only occur if you fail to reject H0. D. The level of significance is the probability of Type II error
When sample size increases, both α and β may decrease.
In testing a proportion, which of the following statements is incorrect? A. Using α = .05 rather than α = .01 would make it more likely that H0 will be rejected. B. When the sample proportion is p = .02 and n = 150, it is safe to assume normality. C. An 80 percent confidence interval is narrower than the 90 percent confidence interval, ceteris paribus. D. The sample proportion may be assumed approximately normal if the sample is large enough. We want at least 10 "successes," but np = 3 in this example.
When the sample proportion is p = .02 and n = 150, it is safe to assume normality.
As you are crossing a field at the farm, your country cousin Jake assures you, "Don't worry about that old bull coming toward us. He's harmless." As you consider Jake's hypothesis, what would be Type I error on your part? A. You will soon feel the bull's horns. B. You will run away for no good reason. C. Jake will not have any more visits from you. Type I error is rejecting Jake's advice when he was right
You will run away for no good reason.
A two-tailed hypothesis test for H0: π = .30 at α = .05 is analogous to: A. asking if the 90 percent confidence interval for π contains .30. B. asking if the 95 percent confidence interval for π contains .30. C. asking if the p-value (area in both tails combined) is less than .025. D. asking if the p-value (area in both tails combined) is less than .10.
asking if the 95 percent confidence interval for π contains .30.
The power of a test is the probability of: A. concluding H1 when H1 is true. B. concluding H1 when H0 is true. C. concluding H0 when H0 is true. D. concluding H0 when H1 is true.
concluding H1 when H1 is true.
The critical value in a hypothesis test: A. is calculated from the sample data. B. usually is .05 or .01 in most statistical tests. C. separates the acceptance and rejection regions. D. depends on the value of the test statistic.
separates the acceptance and rejection regions
Hypothesis tests for a mean using the critical value method require: A. using a two-tailed test. B. sampling a normal population. C. knowing the true population mean. D. specifying α in advance
specifying α in advance
The level of significance is not: A. the probability of a "false rejection." B. a value between 0 and 1. C. the likelihood of rejecting the null hypothesis when it is true. D. the chance of accepting a true null hypothesis.
the chance of accepting a true null hypothesis
"I believe your airplane's engine is sound," states the mechanic. "I've been over it carefully, and can't see anything wrong. I'd be happy to tear the engine down completely for an internal inspection at a cost of $1,500. But I believe that roughness you heard in the engine on your last flight was probably just a bit of water in the fuel, which passed harmlessly through the engine and is now gone." As the pilot considers the mechanic's hypothesis, the cost of Type I error is: A. the pilot will experience the thrill of no-engine flight. B. the pilot will be out $1,500 unnecessarily. C. the mechanic will lose a good customer. D. impossible to determine without knowing α
the pilot will be out $1,500 unnecessarily.