# Mathematics

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. = 0.05 for a two-tailed test.

±2.575

1.764

±1.96

±1.645

Question 2

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. = 0.09 for a right-tailed test.

±1.96

1.34

±1.96

1.34

±1.34

1.96

Question 3

Find the value of the test statistic z using z = The claim is that the proportion of drowning deaths of children attributable to beaches is more than 0.25, and the sample statistics include n = 681 drowning deaths of children with 30% of them attributable to beaches.

3.01

3.01

2.85

-2.85

-3.01

Question 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 left-tailed test is z = -1.83.

0.0672; reject the null hypothesis

0.0336; reject the null hypothesis

0.9664; fail to reject the null hypothesis

0.0672; fail to reject the null hypothesis

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 two-tailed test is z = -1.63.

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

Question 6

Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. The owner of a football team claims that the average attendance at games is over 694, and he is therefore justified in moving the team to a city with a larger stadium. 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.

There is not sufficient evidence to support the claim that the mean attendance is less than 694.

There is sufficient evidence to support the claim that the mean attendance is greater than 694.

There is sufficient evidence to support the claim that the mean attendance is less than 694.

There is not sufficient evidence to support the claim that the mean attendance is greater than 694.

Question 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 medical researcher claims that 6% of children suffer from a certain disorder. Identify the type I error for the test.

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%.

Question 8

Find the P-value for the indicated hypothesis test. In a sample of 88 children selected randomly from one town, it is found that 8 of them suffer from asthma. Find the P-value for a test of the claim that the proportion of all children in the town who suffer from asthma is equal to 11%.

0.2843

-0.2843

0.2157

0.5686

Question 9

Find the critical value or values of based on the given information. H0: = 8.0 n = 10 = 0.01

2.088, 21.666

1.735, 23.589

23.209

21.666

Question 10

Find the critical value or values of based on the given information. H1: > 3.5 n = 14 = 0.05

22.362

22.362

5.892

24.736

23.685

5.892