Rasmussen STA3140 final exam 2016

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Find the critical value zα/2 that corresponds to a degree of confidence of 98%.

Select one:

a. 1.75

b. 2.33

c. 2.05

d. 2.575

Question 2

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Find the margin of error for the 95% confidence interval used to estimate the population proportion.

n = 163, x = 96

Select one:

a. 0.0755

b. 0.00291

c. 0.132

d. 0.0680

Question 3

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Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.

n = 165, x = 138; 95 percent

Select one:

a. 0.779 < p < 0.892

b. 0.791 < p < 0.881

c. 0.780 < p < 0.893

d. 0.790 < p < 0.882

Question 4

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Find the minimum sample size you should use to assure that your estimate of will be within the required margin of error around the population p.

Margin of error: 0.04; confidence level: 99%; from a prior study, estimated by 0.13

Select one:

a. 272

b. 19

c. 469

d. 563

Question 5

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459 randomly selected light bulbs were tested in a laboratory, 291 lasted more than 500 hours.

Find a point estimate of the true proportion of all light bulbs that last more than 500 hours.

Select one:

a. 0.388

b. 0.366

c. 0.634

d. 0.632

Question 6

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A researcher is interested in estimating the proportion of voters who favor a tax on e-commerce.

Based on a sample of 250 people, she obtains the following 99% confidence interval for the population proportion p:

0.113 < p < 0.171

Which of the statements below is a valid interpretation of this confidence interval?

Select one:

a. There is a 99% chance that the true value of p

lies between 0.113 and 0.171.

b. If many different samples of size 250 were selected and, based on each sample, a confidence interval was constructed, in the long run 99% of the confidence intervals would contain the true value of p.

c. If 100 different samples of size 250 were selected and, based on each sample, a confidence interval was constructed, exactly 99 of these confidence intervals would contain the true value ofp.

d. If many different samples of size 250 were selected and, based on each sample, a confidence interval was constructed, 99% of the time the true value of p would lie between 0.113 and 0.171.

Question 7

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Use the confidence level and sample data to find the margin of error E. College students' annual earnings: 99% confidence; n = 74, = $3967, s = $874

Select one:

a. $1187

b. $237

c. $9

d. $262

Question 8

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Use the confidence level and sample data to find a confidence interval for estimating the population m. A group of 56 randomly selected students have a mean score of 30.8 with a standard deviation of 4.5 on a placement test. What is the 90 percent confidence interval for the mean score, m, of all students taking the test?

Select one:

a. 29.6 < m < 32.0

b. 29.8 < m < 31.8

c. 29.2 < m < 32.4

d. 29.4 < m < 32.2

Question 9

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Use the margin of error, confidence level, and standard deviation s to find the minimum sample size required to estimate an unknown population mean .

Margin of error: $139, confidence level: 95%, s = $513

Select one:

a. 3

b. 5

c. 46

d. 53

Question 10

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Do one of the following, as appropriate: (a) Find the critical value zα/2, (b) find the critical value tα/2, (c) state that neither the normal nor the t distribution applies.

99%; n = 17; s is unknown; population appears to be normally distributed.

Select one:

a. zα/2= 2.575

b. tα/2= 2.921

c. tα/2 = 2.898

d. neither

Question 11

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Identify the null hypothesis H0 and the alternative hypothesis H1. A researcher claims that 62% of voters favor gun control.

Select one:

a. H0: p ≥ 0.62 
H1: p < 0.62 
b. H0: p = 0.62 
H1: p ≠ 0.62 
c. H0: p ≠ 0.62 
H1: p = 0.62 
d. H0: p < 0.62 
H1: p ≥ 0.62

Question 12

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Assume that the data has a normal distribution and the number of observations is greater than 50. Find the critical z value used to test a null hypothesis.

α = 0.05 for a left-tailed test.

Select one:

a. ±1.645

b. -1.645

c. -1.96

d. ±1.96

Question 13

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Use the given information to find the P-value. The test statistic in a right-tailed test is z = 1.43.

Select one:

a. 0.4236

b. 0.0434

c. 0.0764

d. 0.5000

Question 14

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Determine whether the hypothesis test involves a sampling distribution of means that is a normal distribution, Student t distribution or neither.

Claim: µ = 977. Sample data: n = 25, x-bar = 984, s = 25. The sample data appear to come from a normally distributed population with  s = 28.

Select one:

a. Student t

b. Neither

c. Normal

Question 15

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Identify the null hypothesis and the alternative hypothesis .

A cereal company claims that the means weight of the cereal in its packets is at least 14 oz.

Select one:

a. H0: µ > 14

H1: µ K 14

b. H0: µ < 14

H1: µ L 14

c. H0: µ = 14

H1: µ < 14

d. H0: µ = 14

H1: µ > 14

Question 16

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A medical school claims that more than 28% of its students plan to go onto general practice. It is found that among a random sample of 130 of the school’s students, 32% of them plan to go into general practice. Find the P-value for a test of the school’s claim.

Select one:

a. 0.1539

b. 0.3078

c. 0.1635

d. 0.3461

Question 17

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Find the critical value or values of based on the given information.

H1: s > 26.1, n = 9, α = 0.01

Select one:

a. 20.090

b. 2.088

c. 1.646

d. 21.666

Question 18

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Assume that a hypothesis is test of a given claim will be conducted. Identify the type I error for the test.

Select one:

a. The error of rejecting the hypothesis that the mean is more than 30 miles per gallon when it is really more than 30 miles per gallon.

b. The error of rejecting the hypothesis that the mean is 30 miles per gallon when it really is greater than 30 miles per gallon.

c. The error of failing to reject the hypothesis that the mean is 30 miles per gallon when it is actually greater than 30 miles per gallon.

d. The error of failing to reject the hypothesis that the mean is equal to 30 miles per gallon when it is actually 30 miles per gallon.

Question 19

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Find the number of successes x suggested by the given statement. A computer manufacturer randomly selects 2360 of its computers for quality assurance and finds that 2.54% of these computers are found to be defective.

Select one:

a. 63

b. 60

c. 65

d. 58

Question 20

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From the sample statistics, find the value of used to test the hypothesis that the population proportions are equal.

n1 = 507

n2 = 140

x1 = 194

x2 = 35

Select one:

a. 0.566

b. 0.257

c. 0.353

d. 0.642

Question 21

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Compute the test statistic used to test the null hypothesis that . In a vote on the Clean Water bill, 41% of the 2005 Democrats voted for the bill while 40% of the 230 republicans voted on the bill.

Select one:

a. 0.233

b. 0.180

c. 0.127

d. 0.211

Question 22

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Determine whether the samples are independent or consist of matched pairs (dependent samples). The effectiveness of a new headache medicine is tested by measuring the amount of time before the headache is cured for patients who use the medicine and another group of patients who use a placebo drug.

Select one:

a. Independent Samples

b. Matched pairs

Question 23

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The two data sets are dependent. Find to the nearest tenth.

x 12.9 11.3 10.7 12.9 12.9

y 12.6 12.6 10.0 10.7 12.3

Select one:

a. 0.3

b. 0.7

c. 0.5

d. 0.6

Question 24

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Assume that you want to test the claim that the paired data come from a population for which the mean difference is . Compute the value of the test statistic.

x 11 5 13 5 9

y 8 7 9 6 4

Select one:

a. t = 2.890

b. t = 0.578

c. t = 1.292

d. t = 0.415

Question 25

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Given the linear correlation coefficient r and the sample size n, determine the critical value of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05.

r = -0.568, n = 25

Select one:

a. Critical values: r = ±0.396, significant linear correlation

b. Critical values: r = ±0.487, significant linear correlation

c. Critical values: r = ±0.487, no significant linear correlation

d. Critical values: r = ±0.396, no significant linear correlation

Question 26

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The regression equation relating to attitude rating(x) and job performance rating (y) for the employees of a company is y^ = 11.7 + 1.02x. Ten pairs of data were used to obtain the equation. The same data yield r = 0.863 and y = 80.1 . What is the best predicted job performance rating for a person whose attitude rating is 70?

Select one:

a. 80.1

b. 81.9

c. 83.1

d. 12.6

Question 27

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The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, µ, of 48°F, ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is incorrect.

Select one:

a. H0: µ = 48°

H1: µ = 48°

b. H0: µ≤ 48°

H1: µ > 48°

c. H0: µ = 48°

H1: µ ≠ 48°

d. H0: µ ≥ 48°

H1: µ< 48°

Question 28

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Use the given information to find the coefficient of determination. Find the coefficient of determination, given that the value of the linear correlation coefficient, r is -0.721.

Select one:

a. 0.520

b. 0.480

c. 0.279

d. 0.721

Question 29

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Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary.

x 1 3 13 7 9

y 143 116 100 98 90

Select one:

a. y^ = 150.7 – 6.8x

b. y^ = -150.7 + 6.8x

c. y^ = 132.79 - 3.54 x

d. y^ = 140.4 – 6.2x

Question 30

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A researcher wishes to test whether the proportion of college students who smoke is the same in four different colleges. She randomly selects 100 students from each college and records the number that smoke. The results are shown below.

                        College A                    College B                    College C                    College D

Smoke             17                               26                                11                                34

Don't smoke    83                                74                                89                                66

Use a 0.01 significance level to test the claim that the proportion of students smoking is the same at all four colleges if the test statistic: x² = 17.832.

Select one:

a. Reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the proportion of students smoking is the same at all four colleges.

b. Do not reject the null hypothesis. There is insufficient evidence to warrant rejection of the claim that the proportion of students smoking is the same at all four colleges.

c. Do not reject the null hypothesis. There is in sufficient evidence to warrant rejection of the claim that the proportion of students smoking is the same at all four colleges.

d. Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the proportion of students smoking is the same at all four colleges.