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Question 1

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.
= 0.05 for a two-tailed test.
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.
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.
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.
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.
Question 6

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.
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.
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%.
9. Find the critical value or values of based on the given information.
H0: = 8.0
n = 10
= 0.01
10. Find the critical value or values of based on the given information.
H1: < 0.14
n = 23
= 0.10
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.
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
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.

Solve the problem.
The table shows the number of pitchers with E.R.A’s below 3.5 in a random sample of sixty pitchers from the National League and in a random sample of fifty-two pitchers from the American League. Assume that you plan to use a significance level of alpha = 0.05 to test the claim that Find the critical value(s) for this hypothesis test. Do the data support the claim that the proportion of National League pitchers with an E.R.A. below 3.5 differs from the proportion of American League pitchers with an E.R.A. below 3.5?

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 P-value for the hypothesis test.
n1 = 100;n2 = 100
x1 = 38;x2 = 40
14. 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.
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.
Two types of flares are tested and their burning times are recorded. The summary statistics are given below.

State what the given confidence interval suggests about the two population means.
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.
The following 98% confidence interval was obtained for mu1 – mu2,
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. Also assume that the population standard deviations are equal (sigma1 = sigma2), so that the standard error of the difference between means is obtained by pooling the sample variances.
A researcher was interested in comparing the amount of time spent watching television by women and by men. Independent simple random samples of 14 women and 17 men were selected and each person was asked how many hours he or she had watched television during the previous week. The summary statistics are as follows.