Posted: November 29th, 2022

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

a = 0.05 for a two-tailed test. (Points : 5)

±2.575

1.764

±1.96

±1.645

**2. **Find the value of the test statistic z using z =

A claim is made that the proportion of children who play sports is less than 0.5, and the sample statistics include n = 1671 subjects with 30% saying that they play a sport. (Points : 5)

3.38

16.35

-33.38

-16.35

**3. **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 = 0.52. (Points : 5)

0.6030; fail to reject the null hypothesis

0.3015; fail to reject the null hypothesis

0.3015; reject the null hypothesis

0.0195; reject the null hypothesis

**4. **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 two-tailed test is z = -1.63. (Points : 5)

0.1032; fail to reject the null hypothesis

0.0516; reject the null hypothesis

0.0516; fail to reject the null hypothesis

0.9484; fail to reject the null hypothesis

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

A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO, p, is less than 2 in every ten thousand. 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. (Points : 5)

There is sufficient evidence to support the claim that the true proportion is less than 2 in ten thousand.

There is sufficient evidence to support the claim that the true proportion is greater than 2 in ten thousand.

There is not sufficient evidence to support the claim that the true proportion is greater than 2 in ten thousand.

There is not sufficient evidence to support the claim that the true proportion is less than 2 in ten thousand.

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

A medical researcher claims that 6% of children suffer from a certain disorder. Identify the type I error for the test. (Points : 5)

Reject the claim that the percentage of children who suffer from the disorder is different from 6% when that percentage really is different from 6%.

Reject the claim that the percentage of children who suffer from the disorder is equal to 6% when that percentage is actually 6%.

Fail to reject the claim that the percentage of children who suffer from the disorder is equal to 6% when that percentage is actually 6%.

Fail to reject the claim that the percentage of children who suffer from the disorder is equal to 6% when that percentage is actually different from 6%.

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

A cereal company claims that the mean weight of the cereal in its packets is 14 oz. Identify the type I error for the test. (Points : 5)

Reject the claim that the mean weight is 14 oz when it is actually greater than 14 oz.

Fail to reject the claim that the mean weight is 14 oz when it is actually different from 14 oz.

Reject the claim that the mean weight is 14 oz when it is actually 14 oz.

Reject the claim that the mean weight is different from 14 oz when it is actually 14 oz.

**8. **Find the P-value for the indicated hypothesis test.

In a sample of 47 adults selected randomly from one town, it is found that 9 of them have been exposed to a particular strain of the flu. Find the P-value for a test of the claim that the proportion of all adults in the town that have been exposed to this strain of the flu is 8%. (Points : 5)

0.0048

0.0024

0.0262

0.0524

**9. **Find the critical value or values of

based on the given information.

H0:

σ = 8.0

n = 10

= 0.01 (Points : 5)

2.088, 21.666

1.735, 23.589

23.209

21.666

**10. **Find the critical value or values of

based on the given information.

H1:

< 0.14

n = 23

= 0.10 (Points : 5)

14.042

14.848

-30.813

30.813

**11. **Find the number of successes x suggested by the given statement.

Among 660 adults selected randomly from among the residents of one town, 30.2% said that they favor stronger gun-control laws. (Points : 5)

200

197

199

198

**12. **Assume that you plan to use a significance level of alpha = 0.05 to test the claim that p1 = p2, Use the given sample sizes and numbers of successes to find the pooled estimate

Round your answer to the nearest thousandth.

n1 = 100; n2 = 100

x1 = 32; x2 = 33 (Points : 5)

0.293

0.227

0.358

0.325

**13. **Assume that you plan to use a significance level of alpha = 0.05 to test the claim that p1 = p2. Use the given sample sizes and numbers of successes to find the z test statistic for the hypothesis test.

n1 = 155; n2 = 146

x1 = 68; x2 = 59 (Points : 5)

z = 7.466

z = 0.435

z = 0.607

z = 13.865

**14. **Assume that you plan to use a significance level of alpha = 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 = 100; n2 = 100

x1 = 38; x2 = 40 (Points : 5)

0.0412

0.1610

0.7718

0.2130

**15. **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.

x1 = 22, n1 = 38 and x2 = 31, n2 = 52; Construct a 90% confidence interval for the difference between population proportions p1 – p2. (Points : 5)

0.406 < p1 – p2 < 0.752

-0.190 < p1 – p2 < 0.156

0.373 < p1 – p2 < 0.785

0.785 < p1 – p2 < 0.373

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