# Hypothesis testing problems

Question 1

The SAT scores of entering freshmen at X University have a normal distribution with mean μ1 = 1200 and standard deviation σ1 = 90, while the SAT scores of entering freshmen at Y University have a normal distribution with mean μ2 = 1215 and standard deviation σ2 = 110. Independent random samples of 100 freshmen are selected from each university. The probability that the sample mean from X University exceeds the sample mean from Y University is

1)0.1446.

2)0.0475.

3)0.2913

4)0.8554.

Question 2

A sociologist is studying the effect on the divorce rate of having children within the first three years of marriage. She selects a random sample of 400 couples who were married for the first time between 1990 and 1995 with both members of the couple aged 20 to 25. Of the 400 couples, 220 had at least one child within the first three years of marriage. Of the couples who had children, 83 were divorced within five years, while of the couples who didn't have children, 52 were divorced within five years. Let p1 and p2 be the proportions of couples married in this time frame and divorced within five years who had children and didn't have children, respectively. The sociologist hypothesized that having children early would increase the likelihood of a couple being divorced. She tested H0: p1 = p2 against the one-sided alternative Ha: p1 > p2 and obtained a P-value of 0.0314. Which of the following statements is a correct interpretation of this result?

1) If you want to reduce your chances of getting divorced, it is best not to marry until you are closer to 30 years of age.

2) If you want to reduce your chances of getting divorced, it is best to wait several years before having children.

3) You have a better chance of staying married if yo do not have children.

4) There is evidence of an association between having children early in a marriage and divorce rate.

Question 3

For a simple random sample of 100 cars of a certain popular model in 2003, it was found that 20 had a certain minor defect in the brakes. For an independent SRS of 400 cars of the same model in 2004, it was found that 50 had the same defect. Let p1 and p2 be the proportions of all cars of this model in 2003 and 2004, respectively, that have the defect. We wish to test H0: p1 = p2 against Ha: p1 > p2. For this test, the (approximate) P-value is

1)0.1345

2)0.0418.

3)0.0536.

4)0.0268.

Question 4

When testing a hypothesis, you are actually,

1) finding out whether there is a real difference between two sample statistics.

2) evaluating the sizes of the population statistics (e.g. the mean or proportion).

3) finding an estimate of the probability that the difference between two statistics is 0.

4) None of the above.

Question 5

In hypothesis testing the null hypothesis

1)the problems in the book will always state a null hypothesis.

2)the alternative hypothesis is the hypothesis that says nothing is happening.

3)you choose a null hypothesis based on whether or not you want to find good results.

4)you should use a two-tailed test if you are unsure about whether a one or two-tailed test is appropriate.

Question 6

You are taking a quiz with 10 multiple choice questions and each questions has 4 possible answers. If you assume that the questions are independent, what is the standard deviation for quiz scores?

1)less than 1.

2)1.875

3)1.37

4)2.68

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#### Solution Summary

The solution provides step by step method for the calculation of test statistic for hypothesis testing . Formula for the calculation and Interpretations of the results are also included.

One and Two Tailed Tests: Hypothesis Testing Problem

Ho: u = 50

H1: u not = 50

The sample mean is 49, and the sample size is 36. the population standard deviation is 5. Use the .05 significance level.

a. Is this a one or two tailed test.

b. What is the decision rule?

c. What is the value of the test statistic?

d. What is your decision regarding Ho?

e. What is the p-value? Interpret it.