# Statistics | Mathematics homework help

Assume that you plan to use a significance level of α = 0.05 to test the claim that p1 = p2. Use the given sample sizes and numbers of successes to find the pooled estimate p. Round your answer to the nearest thousandth.

n1 = 100               n2 = 100               x1 = 42                  x2 = 45

Select one:

a. 0.435

b. 0.392

c. 0.305

d. 0.479

Question 2

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Construct the indicated confidence interval for the difference between population proportions p1 – p2. Assume that the samples are independent and that they have been randomly selected.  In a random sample of 300 women, 45% favored stricter gun control legislation. In a random sample of 200 men, 25% favored stricter gun control legislation. Construct a 98% confidence interval for the difference between the population proportions p1 – p2.

Select one:

a. 0.102 < p1 – p2 < 0.298

b. 0.114 < p1 – p2 < 0.286

c. 0.118 < p1 – p2 < 0.282

d. 0.092 < p1 – p2 < 0.308

Question 3

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Construct the indicated confidence interval for the difference between the two population means. 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.   Independent samples from two different populations yield the following data.

x1 = 958, x2 = 157, s1 = 77, s2 = 88.

The sample size is 478 for both samples. Find the 85% confidence interval for μ1 – μ2.

Select one:

a. 794 < μ1 – μ2 < 808

b. 800 < μ1 – μ2 < 802

c. 793.2946 < μ1 – μ2 < 808.7054

d. 781 < μ1 – μ2 < 821

Question 4

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Assume that you plan to use a significance level of α = 0.05 to test the claim that p1 = p2. Use the given sample sizes and numbers of successes to find the P-value for the hypothesis test.

n1 = 50                  n2 = 50                  x1 = 8                    x2 = 7

Select one:

a. 0.3897

b. 0.7794

c. 0.6103

d. 0.2206

Question 5

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A paint manufacturer made a modification to a paint to speed up its drying time. Independent simple random samples of 11 cans of type A (the original paint) and 9 cans of type B (the modified paint) were selected and applied to similar surfaces. The drying times, in hours, were recorded.

The summary statistics are as follows.

Type A                                   Type B

x1 = 76.3 hrs                       x2 = 65.1 hrs

s1 = 4.5 hrs                          s2 = 5.1 hrs

n1 = 11                                  n2 = 9

The following 98% confidence interval was obtained for μ1 – μ2, the difference between the mean drying time for paint cans of type A and the mean drying time for paint cans of type B:

4.90 hrs < μ1 – μ2 < 17.50 hrs

What does the confidence interval suggest about the population means?

Select one:

a. The confidence interval includes 0 which suggests that the two population means might be equal. There doesn’t appear to be a significant difference between the mean drying time for paint type A and the mean drying time for paint type B. The modification does not seem to be effective in reducing drying times.

b. The confidence interval includes only positive values, which suggests that the mean drying time for paint type A is smaller than the mean drying time for paint type B. The modification does not seem to be effective in reducing drying times.

c. The confidence interval includes only positive values which suggests that the mean drying time for paint type A is greater than the mean drying time for paint type B. The modification seems to be effective in reducing drying times.

d. The confidence interval includes only positive values, which suggests that the two population means might be equal. There doesn’t appear to be a significant difference between the mean drying time for paint type A and the mean drying time for paint type B. The modification does not seem to be effective in reducing drying times.

Question 6

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When performing a hypothesis test for the ratio of two population variances, the upper critical F value is denoted FR. The lower critical F value, FL, can be found as follows: interchange the degrees of freedom, and then take the reciprocal of the resulting F value found in table A -5. FR can be denoted Fα/2 and FL can be denoted F1-α/2 .

Find the critical values FL and FR for a two-tailed hypothesis test based on the following values:

n1 = 25, n2 = 16, α = 0.10

Select one:

a. 0.7351, 2.2378

b. 0.4745, 2.2878

c. 0.5327, 2.2878

d. 0.4745, 2.4371

Question 7

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Consider the set of differences between two dependent sets: 84, 85, 83, 63, 61, 100, 98. Round to the nearest tenth.

Select one:

a. 15.7

b. 15.3

c. 16.2

d. 13.1

Question 8

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Determine the decision criterion for rejecting the null hypothesis in the given hypothesis test; i.e., describe the values of the test statistic that would result in rejection of the null hypothesis.

We wish to compare the means of two populations using paired observations. Suppose that d-bar = 3.125, Sd = 2.911, and n = 8, and that you wish to test the following hypothesis at the 10% level of significance:

H0: μd = 0 against H1: μd > 0.

What decision rule would you use?

Select one:

a. Reject H0 if test statistic is greater than -1.415 and less than 1.415.

b. Reject H0 if test statistic is less than 1.415.

c. Reject H0 if test statistic is greater than 1.415.

d. Reject H0 if test statistic is greater than -1.415.

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

A     69     66     61     63     51

B     25     23     20     25     22

Select one:

a. 50.7

b. 39.0

c. 23.4

d. 48.8

Question 10

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Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is μd = 0. Compute the value of the t test statistic. Round intermediate calculations to four decimal places as needed and final answers to three decimal places as needed.

x   28     31     20     25    28    27    33    35

y   26     27     26     25    29    32    33    34

Select one:

a. t = -0.185

b. t = -0.523

c. t = -1.480

d. t = 0.690

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