155ST3C7­10 Problems from Sample Test 3

1

April 27, 2011

MAT 155 Statistical AnalysisDr. Claude Moore

Cape Fear Community College

Review for Test 3Chapters 7, 8, 9, & 10

Problems from Sample Test 3

1. Construct a 95% confidence interval for the population proportion p with the sample data n = 53 andx = 15.

﴾a﴿ ﴾ 0.162, 0.404﴿ ﴾b﴿ ﴾ 0.18, 0.386﴿ ﴾c﴿ ﴾ 0.161, 0.405﴿ ﴾d﴿ ﴾ 0.181, 0.385﴿

2. Find the critical value t for a confidence level of 99 and a sample size of 17.﴾a﴿ 2.567 ﴾b﴿ 2.583 ﴾c﴿ 2.921 ﴾d﴿ 2.898

2.921

3. Identify the null hypothesis H0 and the alternative hypothesis H1. Use μ for a claim about a mean, p for aclaim about a proportion, and σ for a claim about standard deviation. A researcher claims that the amountsof acetaminophen in a certain brand of cold tablets have a standard deviation different from 3.3 mg.﴾a﴿ H0: σ ≥ 3.3 mg H

1

: σ < 3.3 mg ﴾b﴿ H0: σ ≠ 3.3 mg H

1

: σ = 3.3 mg﴾c﴿ H0: σ ≤ 3.3 mg H

1

: σ > 3.3 mg ﴾d﴿ H0: σ = 3.3 mg H

1

: σ ≠ 3.3 mg

4. Formulate the indicated conclusion by using the flow chart from the formula card. Be sure to address theoriginal claim. A psychologist claims that more than 37 percent of the population suffers from professionalproblems due to extreme shyness. Assume that a hypothesis test of the claim has been conducted and that the conclusion is fail to reject the null hypothesis, state the conclusion in non­technical terms.

﴾a﴿ There is not sufficient evidence to support the claim that the true proportion is less than 37 percent.

﴾b﴿ There is sufficient evidence to support the claim that the true proportion is greater than 37 percent.

﴾c﴿ There is sufficient evidence to support the claim that the true proportion is less than 37 percent.

﴾d﴿ There is not sufficient evidence to support the claim that the true proportion is greater than 37 percent.

155ST3C7­10 Problems from Sample Test 3

2

April 27, 2011

5. Compute the value of an appropriate test statistic for the given hypothesis test. You wish to test the claim that μ < 25.0 with a significance level of α = 0.05. In a sample of n = 52, the sample mean is 27.1, and the population standard deviation is 3.3.

﴾a﴿ z = ­4.59 ﴾b﴿ z = 33.09 ﴾c﴿ z = 4.59 ﴾d﴿ z = 0.64

6. Find the critical t­value or values for the given hypothesis, sample size, and significance level. α = 0.01;n = 12; H0: μ = 81.1

﴾a﴿ ±3.106 ﴾b﴿ 2.718 ﴾c﴿ ±2.718 ﴾d﴿ ±3.055

7. Should the statistician use a t distribution, a normal distribution, or neither to test the null hypothesis? In astudy of monthly incomes, x = 4070, σ = 1980, and n = 7. The data has a slight skew to the right.The null hypothesis is: Ho: μ ≤ 4400

﴾a﴿ Normal distribution ﴾b﴿ t distribution ﴾c﴿ Neither

2.575

A slight skew is considered close enough to normal to use normal distribution.

critical value is z = 2.575.

1.98

155ST3C7­10 Problems from Sample Test 3

3

April 27, 2011

x = np = 2690(0.026) = 69.94 = 70 rounded to nearest whole number.

Since this is a left­tailed test, reject H0 if test statistic < critical value.

With α = 0.10 and a left­tailed test, the critical value is z = ­1.28. 2.03

155ST3C7­10 Problems from Sample Test 3

4

April 27, 2011

Left­tailed test; use t test.

Reject H0 if test statistic < critical t­value.

Critical value from Table A­3: t = ­ 2.896.

From Table A­6 with n = 15 and α = 0.05, we find the critical value r = 0.514.

Since | ­0.248| > 0.514 is NOT true, do NOT reject H0. So, there is no significant linear correlation.

Coefficient of determination is r2 = (­0.935)2 = 0.874225.