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1) Determine whether the samples are independent or dependent

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1) Determine whether the samples are independent or dependent.

A data set includes the morning and evening temperature for the last 110 days.

Choose the correct answer below.

A. The samples are independent because there is not a natural pairing between the two samples.

B. The samples are dependent because there is not a natural pairing between the two samples.

C. The samples are independent because there is a natural pairing between the two samples.

D. The samples are dependent because there is a natural pairing between the two samples.

2) A sample of pulse rates of men and women are used to construct a 95% confidence interval for the difference between the two population means, and the result is − 12.2 < μ₁ – μ₂ < − 1.6, where pulse rates of men correspond to population 1 and pulse rates of women correspond to population 2. Express the confidence interval with pulse rates of women being population 1 and pulse rates of men being population 2.

Choose the correct answer below.

A. − 12.2 < μ₁ – μ₂ < − 1.6 1 2

B. − 12.2 < μ₁ – μ₂ < 1.6 1 2

C. − 1.6 < μ₁ – μ₂ < 12.2 1 2

D.    1.6 < μ₁ – μ₂ < 12.2

3) A study was done using a treatment group and a placebo group. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.10 significance level for both parts.

	Treatment	Placebo
m	m1	m2
n	29	31
x	2.31	2.62
s	0.94	0.54

 

a. Test the claim that the two samples are from populations with the same mean.

What are the null and alternative hypotheses?

A. H₀: μ₁ = μ₂

    H₁: μ₁ ≠ μ₂

B. H₀: μ₁ = μ₂

    H₁: μ₁ > μ₂

C. H₀: μ₁ < μ₂

    H₁: μ₁ ≥ μ₂

D. H₀: μ₁ ≠ μ₂

    H₁: μ₁ < μ₂

The test statistic, t, is _________________. (Round to two decimal places as needed.)

The P-value is ____________________ . (Round to three decimal places as needed.)

State the conclusion for the test.

A. Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean.

B. Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean.

C. Fail to reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean.

D. Reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean.

b. Construct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean.

_______________< μ₁ – μ₂ < ________________

(Round to three decimal places as needed.)

4) Researchers conducted a study to determine whether magnets are effective in treating back pain. The results are shown in the table for the treatment (with magnets) group and the sham (or placebo) group. The results are a measure of reduction in back pain. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below.

	Treatment	Sham
m	m1	m2
n	10	10
x	0.54	0.39
s	0.69	1.21

 

a. Use a 0.05 significance level to test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment.

What are the null and alternative hypotheses?

A. H₀: μ₁ ≠ μ₂

    H₁: μ₁ < μ₂

B. H₀: μ₁ < μ₂

    H₁: μ₁ > μ₂

C. H₀: μ₁ = μ₂

    H₁: μ₁ ≠ μ₂

D. H₀: μ₁ = μ₂

    H₁: μ₁ > μ₂

The test statistic, t, is_____________ . (Round to two decimal places as needed.)

The P-value is____________. (Round to three decimal places as needed.)

State the conclusion for the test.

(1) _____________ the null hypothesis. There (2) __________ sufficient evidence to support the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment.

Is it valid to argue that magnets might appear to be effective if the sample sizes are larger?

Since the (3) ________________ for those treated with magnets is (4) _________ the sample mean for those given a sham treatment, it (5) ___________ valid to argue that magnets might appear to be effective if the sample sizes are larger.

b. Construct a confidence interval suitable for testing the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment.

______________< μ₁ – μ₂ < _____________

(Round to three decimal places as needed.)

1) Fail to reject

Reject

2) is not

is

3) sample mean

Sample standard deviation

4) equal to

Less than

Greater than

5) is

Is not

5) A study was done on body temperatures of men and women. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below.

	Men	Women
m	m1	m2
n	11	59
x	97.55°F	97.44°F
s	0.77°F	0.61°F

 

a. Use a 0.01 significance level to test the claim that men have a higher mean body temperature than women. What are the null and alternative hypotheses?

A. H₀: μ₁ ≠ μ₂

    H₁: μ₁ < μ₂

B. H₀: μ₁ = μ₂

    H₁: μ₁ ¹ μ₂

C. H₀: μ₁ ³ μ₂

    H₁: μ₁ < μ₂

D. H₀: μ₁ = μ₂

    H₁: μ₁ > μ₂

The test statistic, t, is ____________. (Round to two decimal places as needed.)

The P-value is _________. (Round to three decimal places as needed.)

State the conclusion for the test.

A. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that men have a higher mean body temperature than women.

B. Reject the null hypothesis. There is not sufficient evidence to support the claim that men have a higher mean body temperature than women.

C. Fail to reject the null hypothesis. There is sufficient evidence to support the claim that men have a higher mean body temperature than women.

D. Reject the null hypothesis. There is sufficient evidence to support the claim that men have a higher mean body temperature than women.

b. Construct a confidence interval suitable for testing the claim that men have a higher mean body temperature than women.

____________ < m₁ - m₂ < ______________

(Round to three decimal places as needed.)

Does the confidence interval support the conclusion found with the hypothesis test?

(1) _________________ because the confidence interval contains (2) ______

1) Yes

No

2) Zero

Only positive values

Only negative values

6) A study was done on skull sizes of humans during different time periods. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below.

	4000 B.C.	A.D. 150
m	m1	m2
n	21	21
x	131.53 mm	132.97 mm
s	5.48 mm	5.25 mm

 

a. Use a 0.01 significance level to test the claim that the mean skull breadth in 4000 B.C is less than the mean skull breadth in A.D 150.

What are the null and alternative hypotheses?

A. H₀: μ₁ ≠ μ₂

    H₁: μ₁ < μ₂

B. H₀: μ₁ = μ₂

    H₁: μ₁ < μ₂

C. H₀: μ₁ = μ₂

    H₁: μ₁ > μ₂

D. H₀: μ₁ = μ₂

    H₁: μ₁ ¹ μ₂

The test statistic, t, is ______________. (Round to two decimal places as needed.)

The P-value is _________________. (Round to three decimal places as needed.)

State the conclusion for the test.

A. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that the mean skull breadth was less in 4000 B.C. than A.D. 150.

B. Fail to reject the null hypothesis. There is sufficient evidence to support the claim that the mean skull breadth was less in 4000 B.C. than A.D. 150.

C. Reject the null hypothesis. There is not sufficient evidence to support the claim that the mean skull breadth was less in 4000 B.C. than A.D. 150.

D. Reject the null hypothesis. There is not sufficient evidence to support the claim that the mean skull breadth was less in 4000 B.C. than A.D. 150.

b. Construct a confidence interval suitable for testing the claim that the mean skull breadth in 4000 B.C is less than the mean skull breadth in A.D 150.

______________ < m₁ - m₂ < ______________

(Round to three decimal places as needed.)

Does the confidence interval support the conclusion of the test?

(1) ___________ because the confidence interval contains (2) ______

1) No

Yes

2) Only negative values

Zero

Only position values.

7) Given in the table are the BMI statistics for random samples of men and women. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.05 significance level for both parts.

	Male BMI	Female BMI
m	m1	m2
n	41	41
x	27.8782	25.5765
s	7.491722	4.649086

 

a. Test the claim that males and females have the same mean body mass index (BMI).

What are the null and alternative hypotheses?

A. H₀: μ₁ ≠ μ₂

    H₁: μ₁ < μ₂

B. H₀: μ₁ = μ₂

    H₁: μ₁ > μ₂

C. H₀: μ₁ ³ μ₂

    H₁: μ₁ < μ₂

D. H₀: μ₁ = μ₂

    H₁: μ₁ ¹ μ₂

The test statistic, t, is ______________. (Round to two decimal places as needed.)

The P-value is ______________. (Round to three decimal places as needed.)

State the conclusion for the test.

A. Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI.

B. Reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI.

C. Fail to reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI.

D. Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI.

b. Construct a confidence interval suitable for testing the claim that males and females have the same mean BMI.

______________ < m₁ - m₂ < __________

(Round the confidence interval support the conclusion of the test?

(1) ______________ because the confidence interval contains (2) _______________

1) Yes

No

2) Zero

Only negative values

Only position values.

8) Listed below are the numbers of years that archbishops and monarchs in a certain country lived after their election or coronation. Treat the values as simple random samples from larger populations. Complete parts (a) and (b) below. All measurements are in years.

Click the icon to view the table of longevities of archbishops and monarchs.

a. Use a 0.01 significance level to test the claim that the mean longevity for archbishops is less than the mean for monarchs after coronation.

What are the null and alternative hypotheses? Assume that population 1 consists of the longevity of archbishops and population 2 consists of the longevity of monarchs.

A. H₀: μ₁ < μ₂

    H₁: μ₁ > μ₂

B. H₀: μ₁ = μ₂

    H₁: μ₁ < μ₂

C. H₀: μ₁ ¹ μ₂

    H₁: μ₁ > μ₂

D. H₀: μ₁ = μ₂

    H₁: μ₁ ¹ μ₂

The test statistic is ______________. (Round to two decimal places as needed.)

The P-value is __________. (Round to three decimal places as needed.)

State the conclusion for the test.

A. Reject the null hypothesis. There is sufficient evidence to support the claim that archbishops have lower mean longevity than monarchs.

B. Reject the null hypothesis. There is not sufficient evidence to support the claim that archbishops have lower mean longevity than monarchs.

C. Fail to reject the null hypothesis. There is sufficient evidence to support the claim that archbishops have lower mean longevity than monarchs.

D. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that archbishops have lower mean longevity than monarchs.

b. Construct a confidence interval suitable for testing the claim that the mean longevity for archbishops is less than the mean for monarchs after coronation.

__________________ < m₁ - m₂ < ____________________

(Round to three decimal places as needed.)

Does the confidence interval support the conclusion of the test?

(1) _______________ because the confidence interval contains (2) ___________

1: Longevities of Archbishops and Monarchs

Archbishops	14 14	15 14	16 12	13 12	16 17	1 16	14 7	17 16	8 9	12 4	12 20	9 16
Monarchs	18	17	14	15	17	16	14	18	15	16	18	17

 

 1) Yes

No

2) Only negative values

Zero

Only positive Values.

9) Listed in the data table are amounts of strontium-90 (in millibecquerels, or mBq, per gram of calcium) in a simple random sample of baby teeth obtained from residents in two cities. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Complete parts (a) and (b) below.

Click the icon to view the data table of strontium-90 amounts.

a. Use a 0.01 significance level to test the claim that the mean amount of strontium-90 from city #1 residents is greater than the mean amount from city #2 residents.

What are the null and alternative hypotheses? Assume that population 1 consists of amounts from city #1 levels and population 2 consists of amounts from city #2.

 A. H₀: μ₁ < μ₂

    H₁: μ₁ > μ₂

B. H₀: μ₁ ¹ μ₂

    H₁: μ₁ > μ₂

C. H₀: μ₁ = μ₂

    H₁: μ₁ ¹ μ₂

D. H₀: μ₁ = μ₂

    H₁: μ₁ > μ₂

The test statistic is ______________. (Round to two decimal places as needed.)

The P-value is ____________________. (Round to three decimal places as needed.)

State the conclusion for the test.

A. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that the mean amount of strontium-90 from city #1 residents is greater.

B. Reject the null hypothesis. There is not sufficient evidence to support the claim that the mean amount of strontium-90 from city #1 residents is greater.

C. Reject the null hypothesis. There is sufficient evidence to support the claim that the mean amount of strontium-90 from city #1 residents is greater.

D. Fail to reject the null hypothesis. There is sufficient evidence to support the claim that the mean amount of strontium-90 from city #1 residents is greater.

b. Construct a confidence interval suitable for testing the claim that the mean amount of strontium-90 from city #1 residents is greater than the mean amount from city #2 residents.

___________________ mBq < m₁ - m₂ < _______________ mBq

(Round to two decimal places as needed.)

Does the confidence interval support the conclusion of the test?

(1) ___________________ because the confidence interval contains (2) ____________

2: More Info

City #1 City #2

104 117

86 69

121 100

112 85

101 85

104 107

213 110

104 111

290 131

100 133

329 101

145 209

1) Yes

No

2) Only negative values

Zero

Only position values.

10) Use the weights of cans of generic soda as sample one, and use the weights of cans of the diet version of that soda as sample two. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Construct a 90% confidence interval estimate of the difference between the mean weight of the cans of generic soda and the mean weight of cans of the diet version of that soda. Does there appear to be a difference between the mean weights?

Click the icon to view the data table of soda weights.

Assume that population 1 is the generic soda and population 2 is the diet soda.

The 90% confidence interval is __________ ounces < μ₁ – μ₂ < _________ ounces.

(Round to four decimal places as needed.)

Does there appear to be a difference between the mean weights?

The mean weight for the generic soda appears to be (1) _____________ the mean weight for the diet variety because the confidence interval contains (2) _________

3: Soda Weights

Weight of Generic SodaWeight of Diet Soda

0.8148 0.8505

0.8483 0.8516

0.8597 0.8429

0.8739 0.8036

0.8686 0.8156

0.8805 0.8021

0.8914 0.8085

0.8856 0.8019

0.8952 0.8075

0.8052 0.8575

0.8132 0.8587

0.8171 0.8748

0.8361 0.8561

0.8413 0.8678

0.8474 0.8542

0.8238 0.8708

0.8492 0.8547

0.8424 0.8549

0.8406 0.8641

0.8469 0.8298

0.8404 0.8107

0.8393 0.8242

0.8142 0.8011

0.8425 0.8429

0.8492 0.8484

0.8595 0.8496

0.8485 0.8324

0.8794 0.8367

0.8881 0.8034

0.8524 0.8182

0.8589 0.8088

0.8555 0.8009

0.8519 0.8156

0.8554 0.8045

0.8518 0.8062

0.8682 0.8129

Weight of Generic Soda Weight of Diet Soda

1) Greater than

Less than

Equal to

2) Only positive values

Only negative values

Zero.

11) Fill in the blank.

Two samples are ____________ if the sample values from one population are not related to or somehow naturally paired or matched with the sample values from the other population.

Two samples are (1) ___________ if the sample values from one population are not related to or somehow naturally paired or matched with the sample values from the other population.

1) Binomial

Matched pairs

Independent

Discrete

12) Fill in the blank.

Two samples are ________________ if the sample values are paired.

Two samples are (1) ____________ if the sample values are paired.

1) Unusual

Dependent

Disjoint

Independent

13) Which of the following is NOT a requirement of testing a claim about two population means when s₁ and s₂ are unknown and not assumed to be equal?

Choose the correct answer below.

A. Either the two sample sizes are large (n₁ > 30 and n₂ > 30) or both samples come from populations having normal distributions, or both of these conditions are satisfied.

B. The two samples are independent.

C. Both samples are simple random samples.

D. The two samples are dependent.

14) Which of the following is NOT true when dealing with independent samples?

Choose the correct answer below.

A. When making an inference about the two means, the P-value and traditional methods of hypothesis testing result in the same conclusion as the confidence interval method.

B. The null hypothesis m₁ = m₂ or m₁ - m₂ = 0 can be tested using the P-value method, the traditional method, or by determining if the confidence interval limits for m₁ - m₂ contain 0.

C. The confidence interval estimate of µ₁ − µ₂ is (x₁ – x₂) -E < (µ₁ − µ₂) < (x₁ – x₂) + E.

D. The variance of the differences between two independent random variables equals the variance of the first random variable minus the variance of the second random variable.

15) Which of the following is NOT an advantage of pooling sample variances?

Choose the correct answer below.

A. Hypothesis tests have more power.

B. We often know that σ₁ = σ₂.

C. Confidence intervals are a little narrower.

D. The number of degrees of freedom is a little higher.