Exam 4
Name___________________________________
**MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.**
**Provide an appropriate response.**
1) A point estimate is the value of a ______________ that estimates the value of a _______________. 1) _____
A) random variable; statistic B) parameter; statistic
C) random variable; parameter D) statistic; parameter
2) Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is put into a fund called an endowment, and the college spends only the interest earned by the fund. A recent survey of eight private colleges in the United States revealed the following endowments (in millions of dollars) 71.3, 41, 233.7, 495.5, 122.5, 177.9, 93.7, and 216.6. What value will be used as the point estimate for the mean endowment of all private colleges in the United States? 2) _____
A) 207.457 B) 1452.2 C) 8 D) 181.525
3) Determine the point estimate of the population mean for the confidence interval with a lower bound of 25 and an upper bound of 35. 3) _____
A) 35 B) 25 C) 30 D) 31
4) Compute the critical value z* that corresponds to a 94% level of confidence. 4) _____
A) 1.96 B) 1.645 C) 2.33 D) 1.88
5) In a sample of 10 randomly selected employees, it was found that their mean height was 63.4 inches. From previous studies, it is assumed that the standard deviation, σ, is 2.4. Compute the 95% confidence interval for μ. 5) _____
A) (59.7, 66.5) B) (58.1, 67.3) C) (61.9, 64.9) D) (60.8, 65.4)
6) True or False As the level of confidence increases the margin of error decreases. 6) _____
A) True B) False
7) The grade point averages for 10 randomly selected students in an algebra class with 125 students are listed below. What is the effect on the width of the confidence interval if the sample size is increased to 20?
2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.8
7) _____
A) It is impossible to tell without more information.
B) The width increases.
C) The width remains the same.
D) The width decreases.
8) Which of the following is not a characteristic of Students' t distribution? 8) _____
A) depends on degrees of freedom.
B) mean of 1
C) symmetric distribution
D) For large samples, the t and z distributions are nearly equivalent.
9) Find the critical t-value that corresponds to 99% confidence and n = 10. 9) _____
A) 1.833 B) 3.250 C) 2.262 D) 2.821
10) When 465 junior college students were surveyed, 135 said that they have previously owned a motorcycle. Find a point estimate for p, the population proportion of students who have previously owned a motorcycle. 10) _____
A) 0.290 B) 0.225 C) 0.409 D) 0.710
11) Many people think that a national lobby's successful fight against gun control legislation is reflecting the will of a minority of Americans. A random sample of 4000 citizens yielded 2250 who are in favor of gun control legislation. Estimate the true proportion of all Americans who are in favor of gun control legislation using a 90% confidence interval. 11) _____
A) 0.4375 ± 0. 4048 B) 0.4375 ± 0.0 129
C) 0.5625 ± 0. 4048 D) 0.5625 ± 0.0 129
12) A private opinion poll is conducted for a politician to determine what proportion of the population favors adding more national parks. How large a sample is needed in order to be 99% confident that the sample proportion will not differ from the true proportion by more than 3%? 12) _____
A) 22 B) 1842 C) 3684 D) 1509
13) The ______________ hypothesis contains the "=" sign. 13) _____
A) explanatory B) null C) alternative D) conditional
14) A hypothesis test is a "two-tailed" if the alternative hypothesis contains a _______ sign. 14) _____
A) < B) > C) D) +
15) A local tennis pro-shop strings tennis rackets at the tension (pounds per square inch) requested by the customer. Recently a customer made a claim that the pro-shop consistently strings rackets at lower tensions, on average, than requested. To support this claim, the customer asked the pro shop to string 11 new rackets at 51 psi. Upon receiving the rackets, the customer measured the tension of each and calculated the following summary statistics In order to conduct the test, the customer selected a significance level of Interpret this value. 15) _____
A) The probability of concluding that the true mean is less than 51 psi when in fact it is equal to 51 psi is only .01.
B) The probability of making a Type II error is 0. 99.
C) There is a 1% chance that the sample will be biased.
D) The smallest value of α that you can use and still reject is 0 .01.
16) If we reject the null hypothesis when the null hypothesis is true, then we have made a 16) _____
A) Type α error B) Correct decision
C) Type II error D) Type I error
17) If we do not reject the null hypothesis when the null hypothesis is in error, then we have made a 17) _____
A) Type I error B) Correct decision
C) Type II error D) Type β error
18) The level of significance, α, is the probability of making a 18) _____
A) Type II error B) Type β error
C) Correct decision D) Type I error
19) When the results of a hypothesis test are determined to be statistically significant, then we _______________ the null hypothesis. 19) _____
A) polarize B) reject
C) compartmentalize D) fail to reject
20) You wish to test the claim that μ 40 at a level of significance of α = 0.01 and are given sample statistics and Compute the value of the test statistic. Round your answer to two decimal places. 20) _____
A) 2.65 B) 1.96 C) 2.12 D) 3.51
21) Given μ = 25, μ 25, and P = 0.028. Do you reject or fail to reject at the 0.01 level of significance? 21) _____
A) not sufficient information to decide
B) fail to reject
C) reject
22) What is a P-value? 22) _____
A) A probability of observing a sample statistic more extreme than the one observed under the assumption that the null hypothesis is true.
B) A probability of observing a population statistic more extreme than the one observed under the assumption that the null hypothesis is false.
C) A probability of observing a sample statistic more extreme than the one observed under the assumption that the null hypothesis is false.
D) A probability of observing a population statistic more extreme than the one observed under the assumption that the null hypothesis is true.
23) True or False Results that are statistically significant are always practically significant. 23) _____
A) True B) False
24) Find the standardized test statistic t for a sample with n = 12, = 14.2, s = 2.2, and α = 0.01 if Round your answer to three decimal places. 24) _____
A) 1.890 B) 1.991 C) 2.001 D) 2.132
25) The business college computing center wants to determine the proportion of business students who have personal computers (PC's) at home. If the proportion exceeds 25%, then the lab will scale back a proposed enlargement of its facilities. Suppose 200 business students were randomly sampled and 65 have PC's at home. Find the rejection region for this test using 25) _____
A) Reject if z > 2.575 or z < -2.575. B) Reject if z > 2.33.
C) Reject if z = 2.33. D) Reject if z < -2.33.
26) How much money does the average professional hockey fan spend on food at a single hockey game? That question was posed to 10 randomly selected hockey fans. The sampled results show that sample mean and standard deviation were $15.00 and $2.95, respectively. Use this information to create a 99% confidence interval for the mean. 26) _____
A) 15 ± 3.106( 2.95/) B) 15 ± 2.821( 2.95/)
C) 15 ± 3.169( 2.95/) D) 15 ± 3.25( 2.95/)
27) The grade point averages for 10 randomly selected junior college students are listed below. Assume the grade point averages are normally distributed. Find a 98% confidence interval for the true mean.
2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.8 27) _____
A) (1.55, 3.53) B) (3.11, 4.35) C) (2.12, 3.14) D) (0.67, 1.81)
28) Classify the two given samples as independent or dependent.
Sample 1 Pre-training blood pressure of 19 people
Sample 2 Post-training blood pressure of 19 people 28) _____
A) dependent B) independent
29) Classify the two given samples as independent or dependent.
Sample 1 The scores of 26 students who took a statistics final
Sample 2 The scores of 26 different students who took a physics final 29) _____
A) independent B) dependent
30) We are interested in comparing the average supermarket prices of two leading colas in the Tampa area. Our sample was taken by randomly going to each of eight supermarkets and recording the price of a six-pack of cola of each brand. The data are shown in the following table. Find a 98% confidence interval for the difference in mean price of brand 1 and brand 2. Assume that the paired data came from a population that is normally distributed.
Price
30) _____
A) (-0.0846, 0.0096) B) (-0.0779, 0.0029)
C) (-0.1768, 0.1018) D) (-0.0722, -0.0028)
31) The degrees of freedom used when testing two independent samples where the population standard deviation is unknown is 31) _____
A) the smaller of - 1 or - 1. B) + - 1.
C) + - 2. D) the larger of - 1 or - 1.
32) Find the standardized test statistic to test the hypothesis that < . Two samples are randomly selected from each population. The sample statistics are given below. Use α = 0.05.
= 35 = 42
= 28.06 = 30.61
= 2.9 = 2.8 32) _____
A) -2.63 B) -1.66 C) -3.16 D) -3.90
33) A study was conducted to determine if the salaries of librarians from two neighboring cities were equal. A sample of 15 librarians from each city was randomly selected. The mean from the first city was $28,900 with a standard deviation of $2300. The mean from the second city was $30,300 with a standard deviation of $2100. Construct a 95% confidence interval for - . 33) _____
A) (-2054, 238) B) (-3125, 325) C) (-4081, 597) D) (-2871, 567)
34) Find the standardized test statistic estimate, z, to test the hypothesis that > . Use α = 0.01. The sample statistics listed below are from independent samples.
Sample statistics = 100, = 38, and = 140, = 50 34) _____
A) 0.638 B) 2.116 C) 0.362 D) 1.324
35) Construct a 95% confidence interval for - for a survey that finds 30% of 240 males and 41% of 200 females are opposed to the death penalty. 35) _____
A) (-0.561, 0.651) B) (-1.532, 1.342)
C) (-1.324, 1.512) D) (-0.200, -0.021)
1) D
2) D
3) C
4) D
5) C
6) B
7) D
8) B
9) D
10) A
11) D
12) B
13) B
14) C
15) A
16) D
17) C
18) D
19) B
20) A
21) B
22) A
23) B
24) A
25) B
26) D
27) A
28) A
29) A
30) B
31) A
32) D
33) B
34) C
35)
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