Test 4 Chapters 8 to 10

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Question #1

A manufacturer uses a new production method to produce steel rods. A random sample of 17 steel rods resulted in lengths with a standard deviation of 4.7 cm. At the 0.10 significance level, test the claim that the new production method has lengths with a standard deviation different from 3.5 cm, which was the standard deviation for the old method.

A There is not sufficient evidence to support the claim that the standard deviation is not different from 3.5 cm.

B There is sufficient evidence to support the claim that the standard deviation is different from 3.5 cm.

C There is not sufficient evidence to support the claim that the standard deviation is different from 3.5 cm.

D There is sufficient evidence to support the claim that the standard deviation is not different from 3.5 cm.

Question #2

Claim: μ > 75.9 . Sample size is 80 and a significance level is 0.1. W hen should you reject H0?

A Reject H0 if the test statistic z > 1.645.

B Reject H0 if the test statistic z > 1.28.

C Reject H0 if the test statistic z > 1.96.

D Reject H0 if the test statistic z > 2.575.

Question #3

Find the standardized test statistic t for a sample with n = 15,  = 5, s = 0.8, and a=0.05 if H0: μ ≤ 4.7 . Round your answer to three decimal places.

A 1.452

B 1.728

C 1.312

D 1.631

Question #4

Find the standardized test statistic t for a sample with n = 12,  = 20.2, s = 2.2, and α = 0.01 if H0: μ = 19. Round your answer to three decimal places.

A 1.991

B 2.132

C 1.890

D 2.001

Question #5

Use the given information to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis).

The test statistic in a right-tailed test is z = 1.43.

A 0.0764; reject the null hypothesis

B 0.0764; fail to reject the null hypothesis

C 0.1528; fail to reject the null hypothesis

D 0.1528; reject the null hypothesis

Question #6

Find the P-value for the indicated hypothesis test.

A medical school claims that more than 28% of its students plan to go into 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.

A 0.3461

B 0.3078

C 0.1539

D 0.1635

Question #7

The test statistic in a two-tailed test is z = 1.95.

A 0.0256; reject the null hypothesis

B 0.0512; fail to reject the null hypothesis

C 0.9744; fail to reject the null hypothesis

D 0.0512; reject the null hypothesis

Question #8

Use the given data to find the best predicted value of the response variable.

The regression equation relating dexterity scores (x) and productivity scores (y) for the employees of a company is ŷ = 5.50 + 1.91x. Ten pairs of data were used to obtain the equation. The same data yield r= 0.986 and ȳ = 56.3. What is the best predicted productivity score for a person whose dexterity score is 38?

A 56.30

B 210.91

C 78.08

D 58.20

Question #9

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

Ten students in a graduate program were randomly selected. Their grade point averages (GPAs) when they entered the program were between 3.5 and 4.0. The following data were obtained regarding their GPAs on entering the program versus their current GPAs.

Entering GPA / Current GPA
3.5/3.6
3.8/3.7
3.6/3.9
3.6/3.6
3.5/3.9
3.9/3.8
4.0/3.7
3.9/3.9
3.5/3.8
3.7/4.0

A ŷ = 4.91 + 0.0212x

B ŷ = 3.67 + 0.0313x

C ŷ = 5.81 + 0.497x

D ŷ = 2.51 + 0.329x

Question #10

Choose the most valid conclusion.
Given: Each school in a state reports the average SAT score of its students. There is a significant linear correlation between the average SAT score of a school and the average annual income in the district in which the school is located.

A Averages supress individual variation and rend to inflate the correlation coefficient. The fact that there is significant linear correlation between the average SAT scores and average incomes in the district does not necessarily imply that there is significant linear correlation between individual SAT scores and family incomes.

B There is a significant linear correlation between individual SAT scores and family income.

Question #11

Find the value of the linear correlation coefficient r.
The paired data below consist of the test scores of 6 randomly selected students and the number of hours they studied for the test.
Hours : 5 -10- 4- 6 -10- 9
Score: 65-88-72-84-57-83

These sums are available to use with the formula. You don’t need them if you are using the calculator.
∑x = 44, ∑x2 = 358, ∑y = 449, ∑y2 = 34347, ∑xy =3314

A 0.131

B 0.869

C 0.123

D 0.236

Question #12

Given the linear correlation coefficient r and the sample size n, determine the critical values 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 = -0.18, n = 15

A Critical values: r = ±0.514, no significant linear correlation

B Critical values: r = 0.514, no significant linear correlation

C Critical values: r = ±0.514, significant linear correlation

D Critical values: r = ±0.532, no significant linear correlation

Question #13

Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim.

A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard deviation different from the σ = 3.3mg claimed by the manufacturer. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.

A There is not sufficient evidence to support the claim that the standard deviation is different from 3.3 mg.

B There is sufficient evidence to support the claim that the standard deviation is different from 3.3 mg.

C There is sufficient evidence to support the claim that the standard deviation is equal to 3.3 mg.

D There is not sufficient evidence to support the claim that the standard deviation is equal to 3.3 mg.

Question #14

Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim.

The principal of a middle school claims that test scores of the seventh-graders at his school vary less than the test scores of the seventh-graders at a neighboring school, which have variation described by σ = 14.7. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.

A There is sufficient evidence to support the claim that the standard deviation is less than 14.7.

B There is not sufficient evidence to support the claim that the standard deviation is less than 14.7.

C There is sufficient evidence to support the claim that the standard deviation is greater than 14.7.

D There is not sufficient evidence to support the claim that the standard deviation is greater than 14.7.

Question #15

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

The principal of a school claims that the percentage of students at his school that come from single-parent homes is 22%. Identify the type II error for the test.

A Reject the claim that the percentage of students that come from single-parent homes is equal to 22% when that percentage is actually less than 22%.

B Fail to reject the claim that the percentage of students that come from single-parent homes is equal to 22% when that percentage is actually different from 22%.

C Fail to reject the claim that the percentage of students that come from single-parent homes is equal to 22% when that percentage is actually 22%.

D Reject the claim that the percentage of students that come from single-parent homes is equal to 22% when that percentage is actually 22%.

Question #16

For the set of hypotheses, use the sample information to compute the appropriate test statistic.

Ho: σ = 5.2 α = 0.01 n = 23 s = 6.1
H1: σ > 5.2

A χ2 = 30.2744

B χ2 = 25.8077

C χ2 = 31.6505

D χ2 = 15.9871

Question #17

Find the critical value or values of χ2 based on the given information.

H1: : σ ≠ 8.0
n = 10
α = 0.01