MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

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

1) A random sample of 105 light bulbs had a mean life of x-bar = 438 hours with a standard deviation of s = 39 hours. Construct a 90 percent confidence interval for the mean life, m, of all light bulbs of this type.

a) ( 428, 448) b) ( 432, 444) c) ( 431, 445) d) ( 429, 447) 2) Find the critical value za/2 that corresponds to a degree of confidence of 98%. a) 2.33 b) 1.75 c) 2.05 d) 2.575 Use the given degree of confidence and sample data to construct a confidence interval for the population mean m.
3) 39 packages are randomly selected from packages received by a parcel service. The sample has a mean weight of 10.0 pounds and a standard deviation of 1.6 pounds. What is the 95 percent confidence interval for the true mean weight, m, of all packages received by the parcel service? a) ( 9.3, 10.7) b) ( 9.6, 10.4) c) ( 9.4, 10.6) d) ( 9.5, 10.5) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.  Solve the problem.
4) The sample data below consists of the heights of 30 randomly selected adults. You wish to use the data to obtain a confidence interval estimate of the population mean. Does the data set include any outliers? How should you handle the outlier in this case? Explain your answer. Are confidence interval limits sensitive to outliers?
60.1 66.9 70.4 73.2 65.2 64.1
68.5 69.2 64.0 62.4 66.9 71.2
682 61.4 65.7 72.5 74.0 70.0
65.8 69.3 60.4 72.4 58.1 68.3
60.5 66.4 60.5 71.3 67.8 73.2


MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.  Assume that a computer was used to generate the given confidence interval for the population mean, m. Find the sample mean or margin of error as specified.

5) 33.2 < m < 55.5 Find the sample mean, x-bar.

a) 43.95 b) 44.35 c) 44.65 d) 33.2 For questions 6 and 7, given the sample statistics, determine if you should use the t distribution, normal distribution, or neither to construct a confidence interval for an estimate of m.
6) From a sample of 92 observations, x-bar = 13.98, s = 3.70. The data do not have a bell-shaped distribution. a) t distribution b) Normal distribution c) Neither 7) From a sample of 22 observations, x-bar = 65.7, s = 3.6. s is unknown, the population appears to be very skewed. a) t distribution b) Normal distribution c) Neither 8) For a sample with 84 observations, the mean is 68 and the standard deviation is 8.9. Use a 95% confidence interval. Find the margin of error. a) 1.71 b) 1.63 c) 1.90 d) 4.10 9) Find the critical value za/2 that corresponds to a confidence level of 95% and a sample size of 23. a) 2.069 b) 2.074 c) 1.717 d) 1.714 Use the given degree of confidence and sample data to construct a confidence interval for the population mean m. Assume that the population has a normal distribution.
10) A sociologist develops a test to measure attitudes about public transportation, and 27 randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4. Construct the 95% confidence interval for the mean score of all such subjects.
a)  69.2 < m < 83.2    c) 74.6 < m < 77.8
b)  67.7 < m < 84.7     d) 64.2 < m < 88.2
11) The weekly earnings of students in one age group are normally distributed with a standard deviation of 75 dollars. A researcher wishes to estimate the mean weekly earnings of students in this age group. Find the sample size needed to assure with 98 percent confidence that the sample mean will not differ from the population mean by more than 5 dollars. a) 1231 b) 1222     c) 82    d) 17 12) The monthly credit card debts for individual accounts are normally distributed with a standard deviation of 25 dollars. A researcher wishes to estimate the mean monthly credit card debt for all individual accounts. Find the sample size needed to assure with 95.44 percent confidence that the sample mean will not differ from the population mean by more than 5 units.
a) 20     b) 4    c) 104     d) 100


13) Weights of women in one age group are normally distributed with a standard deviation s of 12 lb. A researcher wishes to estimate the mean weight of all women in this age group. Find how large a sample must be drawn in order to be 90 percent confident that the sample mean will not differ from the population mean by more than 2.4 lb.

a) 67 b) 97 c) 80 d) 69


14) You wish to estimate the mean weight of machine components of a certain type and you require a 96% degree of confidence that the sample mean will be in error by no more than 0.009 g. After using the range rule of thumb to estimate the standard deviation, find the sample size required. Typical weights range from 8.20 g to 8.40 g.

a) 10 b) 12 c) 130 d) 95 15) When estimating a population mean, if we sample without replacement from a small population, the margin of error, E, should be modified to include a finite population correction factor as follows:  

Use this expression to determine the sample size needed in the following situation:

You wish to estimate the mean height of a population by sampling without replacement from the population. The size of the population is N = 180. You wish to be 96% confident that the sample mean is within 0.8 inches of the true mean. Assume that s = 3.6 inches.
a) 47     b) 67    c) 59     d) 18
 
 

16) A newspaper article about the results of a poll states: "In theory, the results of such a poll, in 99 cases out of 100 should differ by no more than 4 percentage points in either direction from what would have been obtained by interviewing all voters in the United States." Find the sample size suggested by this statement. a) 1037 b) 42 c) 601 d) 849 Find the minimum sample size you should use to assure that your estimate, p-hat, will be within the required margin of error around the population p.
17) A university's administrator proposes to do an analysis of the proportion of graduates who have not found employment in their major field one year after graduation. In previous years, the percentage averaged 0.09. He wants the margin of error to be within 0.03 at a 99% confidence level. a) 18 b) 604 c) 725 d) 350 Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
18) n = 116, x = 58; 88 percent a) ( 0.427, 0.573) b) ( 0.428, 0.572) c) ( 0.423, 0.577) d) ( 0.424, 0.576)


19) Of 315 randomly selected medical students, 23 said that they planned to work in a rural community. Find a 95% confidence interval for the true proportion of all medical students who plan to work in a rural community.

a) 0.0389 < p < 0.107 c) 0.0489 < p < 0.0971

b) 0.0353 < p < 0.111 d) 0.0443 < p < 0.102

  20) Suppose that n trials of a binomial experiment result in no successes. According to the "Rule of Three", we have 95% confidence that the true population proportion has an upper bound of 3/n. If a manufacturer randomly selects 18 computers for quality control and finds no defective computers, what statement can you make by using the rule of three, about the proportion p, of all its computers which are defective? a) We are 95% confident that p does not exceed 1/6.
b) The value of p cannot be greater than 1/6.
c) We are 95% confident that p lies between 1/18 and 1/6.
d) We are 95% confident that p is greater than 1/6.


Identify the null hypothesis H0 and the alternative hypothesis H1. Use m for a claim about a mean, p for a claim about a proportion, and s for a claim about variation.
21) An entomologist writes an article in a scientific journal which claims that fewer than 16 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Use the parameter p, the true proportion of fireflies unable to produce light.

a) H0: p less than 0.0016         H1: p greater than or equal to  0.0016
b) H0: p greater than 0.0016    H1: p less than or equal to  0.0016
c) H0: p greater than or equal to 0.0016     H1: p less than 0.0016
d) H0: p less than or equal to 0.0016          H1: p greater than 0.0016
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.
22) a = 0.03; Null is mgreater than or equal to 290 a) -1.88 b) ±1.88 c) ±2.17 d) 1.88 Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim.
23) The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, m, of 46eF, ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is incorrect. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms. a) There is sufficient evidence to support the claim that the mean temperature is different from 46 degree Farenheit.
b) There is not sufficient evidence to support the claim that the mean temperature is equal to 46 degree Farenheit.
c) There is sufficient evidence to support the claim that the mean temperature is equal to 46 degree Farenheit.
d) There is not sufficient evidence to support the claim that the mean temperature is different from 46 degree Farenheit .


24) A researcher claims that 62% of voters favor gun control. 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.

a) There is not sufficient evidence to support the claim that 62% of voters favor gun control.
b) There is not sufficient evidence to warrant rejection of the claim that 62% of voters favor gun control.
c) There is sufficient evidence to warrant rejection of the claim that 62% of voters favor gun control.
d) There is sufficient evidence to support the claim that more than 62% of voters favor gun control.
Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test.
25) A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard deviation different from the s = 3.3 mg claimed by the manufacturer. Identify the type II error for the test. a) The error of rejecting the claim that the standard deviation is 3.3 mg when it really is 3.3 mg.
b) The error of failing to reject the claim that the standard deviation is 3.3 mg when it is actually different from 3.3 mg.
c) The error of rejecting the claim that the standard deviation is more than 3.3 mg when it really is more than 3.3 mg.
Use the given claim and test statistic to find the P-value.
26) Claim: The mean monthly salary of employees at one company is at most $32,500.  Test statistic: z = 0.52
    a) 0.6030    b) 0.3015    c) 0.3970    d) 0.6985
Compute the value of an appropriate test statistic for the given hypothesis test.
27)  A population is normally distributed with a standard deviation s = 275. We wish to test the hypotheses: Null: less than equal to 33,931;  Alternative: m greater than 33,931.
    A 129-item sample has a mean x-bar = 34,371. Compute the value of the test statistic.
    a) 2820.95     b) 0.14    c) 937.98     d) 18.17


28)  A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a mean different from the 600 mg claimed by the manufacturer. You wish to test this claim at the 0.05 level of significance. The mean acetaminophen content for a random sample of n = 44 tablets is 603.8 mg with a standard deviation of 4.6 mg. Compute the value of the test statistic.

    a) z = 36.35     b) z = 0.83     c) z = 5.48    d) z = 11.75
Determine the decision criterion for rejecting the null hypothesis in the given hypothesis test; i.e., describe the values of the test statistic that would result in rejection of the null hypothesis.
29)  The principal of a middle school claims that mean test score of the seventh-graders at his school is higher than 72.1. You wish to test this claim at the 0.05 level of significance. The mean score for a random sample of 100 seventh-graders is 75.7 with a standard deviation of 15.2. What criterion would be used for rejecting the null hypothesis, that m is less than or eqal to 72.1?
a)  Reject H0 if test statistic > 1.96 or < -1.96.
b)  Reject H0 if test statistic > 1.96.
c)  Reject H0 if test statistic < 1.645.
d)  Reject H0 if test statistic > 1.645.


Solve the problem.
30)  In a hypothesis test, the null hypothesis of m = 60 was not rejected because the P-value was greater than 0.05. The sample size was 65 and the sample mean was 63.5. What can you conclude about the possible range of values for s, the sample standard deviation?

a)  The value of s is greater than 17.15.
b)  The value of s is greater than 14.43.
c) The value of s is less than 14.43.
d)  The value of s is less than 17.15.


What decision rule should you use to test the null hypothesis?


 
 

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Test the given claim by using the p-value method of testing hypotheses. Assume that the sample is a simple random sample selected from a normally distributed population. Include the hypotheses, the test statistic, the p-value, and your conclusion.
32) Test the claim that the mean lifetime of car engines of a particular type is greater than 220,000 miles. Sample data are summarized as n = 23, x-bar = 226,450 miles, and s = 11,500 miles. Use a significance level of a = 0.01.
 
 

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Compute the value of an appropriate test statistic for the given hypothesis test.
33)  A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz. You wish to test this claim at the 0.02 level of significance. The mean weight for a random sample n = 12 cereal packets is 13.4 ounces with a standard deviation of 0.8 ounces. Compute the value of the appropriate test statisic.

a) t = -2.60 b) t = 2.60 c) t = -9.00 d) t = -0.75 Find the critical t value or values for the given hypothesis, sample size, and significance level.
34) Null: m greater than or equal to  91.8   n = 16   a = 0.01

a) -2.921 b) ±2.947 c) -2.583 d) -2.602
 
 

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Test the given claim by using the p-value method of testing hypotheses. Assume that the sample is a simple random sample selected from a normally distributed population. Include the hypotheses, the test statistic, the p-value, and your conclusion.
35)  Test the claim that the mean age of the prison population in one city is less than 26 years. Sample data are summarized as n = 25, x-bar = 24.4 years, and s = 9.2 years. Use a significance level of a= 0.05.

     
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Compute the test statistic used to test the null hypothesis.
36)  The National Transportation Association reports that more accidents are caused by cell phones than by drunken drivers. The cell phone industry did their own study to refute the claim. They obtained 10,000 auto accident reports and found that 16% were caused by drivers using cell phones. If the actual rate for drunken driver accidents is 13%, were the cell phone makers happy with the results? H0: p ? 0.13. Use a 95% confidence level.
    a) 12.400 b) 8.921 c) 3.033 d) 17.841
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Use the traditional method to test the given hypothesis. Assume that all samples have been randomly selected.
37)  A manufacturer considers his production process to be out of control when defects exceed 3%. In a random sample of 85 items, the defect rate is 5.9% but the manager claims that this is only a sample fluctuation and production is not really out of control. At the 0.01 level of significance, test the manager's claim.
 

38)  In a sample of 162 children selected randomly from one town, it is found that 32 of them suffer from asthma. At the 0.05 significance level, test the claim that the proportion of all children in the town who suffer from asthma is 11%.

     
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Compute the test statistic used to test the null hypothesis.
39)  Out of 84 observations, 67% were successes. Null: p = 0.49. Confidence level: 98%.
    a) 0.010 b) 3.300 c) 1.723 d) 1.291
State the decision rule to test the null hypothesis.
40)  The National Transportation Association reports that more accidents are caused by cell phones than by drunken drivers. The cell phone industry did their own study to refute the claim. They obtained 10,000 auto accident reports and found that 12% were caused by drivers using cell phones. If the actual rate for drunken driver accidents is 13%, were the cell phone makers happy with the results? Use a 95% confidence level.