Stat 210 Practice Exam Three (proportions) I

Stat 210

Practice Exam Three (proportions)

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This sample test is too long, but I made it that way to illustrate all of he most common questions your test might have.

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test. 1) A medical researcher claims that 6% of children suffer from a certain disorder. Identify the type I 1) error for the test. A) 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%. B) 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%. C) Reject the claim that the percentage of children who suffer from the disorder is equal to 6% when that percentage is actually 6%. D) 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%.

2) The principal of a school claims that the percentage of students at his school that come from

2)

single-parent homes is 13%. Identify the type II error for the test.

A) Fail to reject the claim that the percentage of students that come from single-parent homes is

equal to 13% when that percentage is actually 13%. B) Fail to reject the claim that the percentage of students that come from single-parent homes is

equal to 13% when that percentage is actually different from 13%. C) Reject the claim that the percentage of students that come from single -parent homes is equal

to 13% when that percentage is actually 13%. D) Reject the claim that the percentage of students that come from single -parent homes is equal

to 13% when that percentage is actually less than 13%.

Find the critical z value. 3) Find z/2 for = 0.08.

A) 1.75

B) 2.65

4) = 0.1 for a two-tailed test.

A) ?2.052

B) ?2.33

C) 1.41 C) ?1.4805

3) D) 1.96

4) D) ?1.645

Solve the problem. 5) The following confidence interval is obtained for a population proportion, p: 0.537 < p < 0.563. Use 5) ^ these confidence interval limits to find the point estimate, p.

A) 0.537

B) 0.555

C) 0.545

D) 0.550

Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the

given statistics and confidence level. Round the margin of error to four decimal places.

6) 95% confidence; n = 2428, x = 1704

6)

A) 0.0204

B) 0.0155

C) 0.0182

D) 0.0246

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Use the given information to find the P-value. 7) The test statistic in a left-tailed test is z = -1.83.

A) 0.0672

B) 0.0672

C) 0.0336

7) D) 0.9664

Solve the problem. Round the point estimate to the nearest thousandth.

8) 22 randomly picked people were asked if they rented or owned their own home, 9 said they

8)

rented. Obtain a point estimate of the proportion of home owners.

A) 0.290

B) 0.636

C) 0.409

D) 0.591

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.

9) n = 110, x = 55; 88% confidence

9)

A) 0.422 < p < 0.578

B) 0.421 < p < 0.579

C) 0.426 < p < 0.574

D) 0.425 < p < 0.575

Use the given data to find the minimum sample size required to estimate the population proportion.

^

10) Margin of error: 0.04; confidence level: 95%; from a prior study, p is estimated by the decimal

10)

equivalent of 89%.

A) 9

B) 708

C) 236

D) 209

11) Margin of error: 0.04; confidence level: 95%; nothing is known about the proportion.

11)

A) 317

B) 501

C) 232

D) 601

Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol (, p, ) for the

indicated parameter.

12) A psychologist claims that more than 4.1 percent of the population suffers from professional

12)

problems due to extreme shyness. Use p, the true percentage of the population that suffers from

extreme shyness. A) H0: p < 4.1%

B) H0: p = 4.1%

C) H0: p > 4.1%

D) H0: p = 4.1%

H1: p 4.1%

H1: p < 4.1%

H1: p 4.1%

H1: p > 4.1%

Find the value of the test statistic z using .

13) The claim is that the proportion of accidental deaths of the elderly attributable to residential falls is 13) more than 0.10, and the sample statistics include n = 800 deaths of the elderly with 15% of them

attributable to residential falls.

A) -3.96

B) 4.71

C) -4.71

D) 3.96

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).

14) With H1: p 0.612, the test statistic is z = -3.06.

14)

A) 0.0011; fail to reject the null hypothesis

B) 0.0022; fail to reject the null hypothesis

C) 0.0022; reject the null hypothesis

D) 0.0011; reject the null hypothesis

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Use want to test the claim that p1 = p2, Use the given sample data to find the pooled estimate p.

15) n1 = 48

n2 = 453

15)

x1 = 8

x2 = 109

A) 0.234

B) 0.187

C) 0.094

D) 0.281

Assume that you plan to use a significance level of = 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.

16) A random sampling of sixty pitchers from the National League and fifty -two pitchers from the

16)

American League showed that 19 National and 11 American League pitchers had E.R.As below

3.5. A) z = 1.629

B) z = 1.253

C) z = 15.457

D) z = 191.183

Assume that you plan to use a significance level of = 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.

17) n1 = 50

n2 = 50

17)

x1 = 8

x2 = 7

A) 0.3897

B) 0.7794

C) 0.6103

D) 0.2206

Solve the problem.

18) The table shows the number of households burglarized in a sample of households with dogs and 18) in a sample of households without dogs. Assume that you plan to use a significance level of = 0.01 to test the claim that p1 < p2. Find the critical value(s) for this hypothesis test. Do the data

support the claim that a smaller proportion of households with pet dogs are burglarized?

Household with Dog Household without Dog

Number of households in sample

206

140

Number of households burglarized

20

11

A) z = -2.575; no

B) z = -2.33; no

C) z = -1.96; yes

D) z = 2.33; yes

Assume that you plan to use a significance level of = 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.

19) n1 = 200

n2 = 100

19)

x1 = 11

x2 = 8

A) 0.0201

B) 0.0012

C) 0.1011

D) 0.4010

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Problem 20 went on vacation, he should be back soon.

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.

21) In a random sample of 500 people aged 20 -24, 22% were smokers. In a random sample of 450

21)

people aged 25-29, 14% were smokers. Construct a 95% confidence interval for the difference

between the population proportions p1 - p2.

A) 0.032 < p1 - p2 < 0.128

B) 0.025 < p1 - p2 < 0.135

C) 0.035 < p1 - p2 < 0.125

D) 0.048 < p1 - p2 < 0.112

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22) A poll of 1068 adult Americans reveals that 48% of the voters surveyed prefer the

22)

Democratic candidate for the presidency. At the 0.05 level of significance, test the claim

that at least half of all voters prefer the Democrat.

a) Write the null and alternative hypothesis in symbolic form (use the correct symbols).

b) Find the critical value(s) c) Draw the curve, label the rejection region(s) and place the critical value(s) on the graph.

d) Find the test statistic e) Determine the p-value. f) State your decision (exactly as we did repeatedly in class)

g) State your conclusion (exactly as we did repeatedly in class)

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