**SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.**
**Provide an appropriate response.**
1) Under what circumstances can you replace σ with s in the formula
2) Define margin of error. Explain the relation between the confidence interval and the error estimate. Suppose a confidence interval is Find the sample mean and the error estimate E.
3) What is the best point estimate for the population proportion? Explain why that point estimate is best. _
**Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim.**
4) According to a recent poll 53% of Americans would vote for the incumbent president. If a random sample of 100 people results in 45% who would vote for the incumbent, test the claim that the actual percentage is 53%. Use a 0.10 significance level.
**Use the traditional method to test the given hypothesis. Assume that the population is normally distributed and that the sample has been randomly selected.**
5) Systolic blood pressure levels for men have a standard deviation of 19.7 mm Hg. A random sample of 31 women resulted in blood pressure levels with a standard deviation of 22.4 mm Hg. Use a 0.05 significance level to test the claim that blood pressure levels for women have the same variation as those for men.
**Test the given claim using the traditional method of hypothesis testing. Assume that the sample has been randomly selected from a population with a normal distribution.**
6) In tests of a computer component, it is found that the mean time between failures is 520 hours. A modification is made which is supposed to increase the time between failures. Tests on a random sample of 10 modified components resulted in the following times (in hours) between failures.
518 548 561 523 536
499 538 557 528 563
At the 0.05 significance level, test the claim that for the modified components, the mean time between failures is greater than 520 hours.
**Solve the problem.**
7) Suppose that you wish to perform a traditional hypothesis test to test a claim regarding two means. Give an example of a situation in which the matched pairs test would be appropriate and give an example of a situation in which it would be appropriate to perform a test for large and independent samples.
**Provide an appropriate response.**
8) Complete the table to describe each symbol.
**Perform the indicated goodness-of-fit test.**
9) A company manager wishes to test a union leader's claim that absences occur on the different week days with the same frequencies. Test this claim at the 0.05 level of significance if the following sample data have been compiled.
**Provide an appropriate response.**
10) Define a point estimate. What is the best point estimate for μ?
**Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim.**
11) A poll of 1,068 adult Americans reveals that 48% of the voters surveyed prefer the 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.
**Use the traditional method to test the given hypothesis. Assume that the samples are independent and that they have been randomly selected**
12) In a random sample of 360 women, 65% favored stricter gun control laws. In a random sample of 220 men, 60% favored stricter gun control laws. Test the claim that the proportion of women favoring stricter gun control is higher than the proportion of men favoring stricter gun control. Use a significance level of 0.05.
**Solve the problem.**
13) Use the P-value method to test the claim that the population standard deviation of the systolic blood pressures of adults aged 40-50 is equal to The sample statistics are as follows: Be sure to state the hypotheses, the value of the test statistic, the P-value, and your conclusion. Use a significance level of 0.05.
**Use the traditional method of hypothesis testing to test the given claim about the means of two populations. Assume that two dependent samples have been randomly selected from normally distributed populations.**
14) Ten different families are tested for the number of gallons of water a day they use before and after viewing a conservation video. At the 0.05 significance level, test the claim that the mean is the same before and after the viewing.
**Perform the indicated goodness-of-fit test.**
15) In studying the occurrence of genetic characteristics, the following sample data were obtained. At the 0.05 significance level, test the claim that the characteristics occur with the same frequency.
16) Among the four northwestern states, Washington has 51% of the total population, Oregon has 30%, Idaho has 11%, and Montana has 8%. A market researcher selects a sample of 1000 subjects, with 450 in Washington, 340 in Oregon, 150 in Idaho, and 60 in Montana. At the 0.05 significance level, test the claim that the sample of 1000 subjects has a distribution that agrees with the distribution of state populations.
**Use a ** ** test to test the claim that in the given contingency table, the row variable and the column variable are independent.**
17) Use the sample data below to test whether car color affects the likelihood of being in an accident. Use a significance level of 0.01.
18) The table below shows the age and favorite type of music of 668 randomly selected people.
Use a 5 percent level of significance to test the null hypothesis that age and preferred music type are independent.
**Solve the problem.**
19) A researcher wishes to test whether the proportion of college students who smoke is the same in four different colleges. She randomly selects 100 students from each college and records the number that smoke. The results are shown below.
Use a 0.01 significance level to test the claim that the proportion of students smoking is the same at all four colleges.
**Test the given claim using the traditional method of hypothesis testing. Assume that the sample has been randomly selected from a population with a normal distribution.**
20) Use a significance level of α = 0.05 to test the claim that μ ≠ 32.6. The sample data consists of 15 scores for which = 41 and .
**MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.**
**Solve the problem.**
21) Find the value of that corresponds to a level of confidence of 97.80 percent.
A) 29 B) 0.011 C) -2 D) 2
22) The following confidence interval is obtained for a population proportion, p:
( 0.509, 0.533)
Use these confidence interval limits to find the point estimate, .
A) 0.509 B) 0.533 C) 0.521 D) 0.528
**Use the confidence level and sample data to find a confidence interval for estimating the population ****μ****.**
23) A group of 65 randomly selected students have a mean score of 31.8 with a standard deviation of 5.4 on a placement test. What is the 90 percent confidence interval for the mean score, μ, of all students taking the test?
A) 30.5 < μ < 33.1 B) 30.1 < μ < 33.5 C) 30.2 < μ < 33.4 D) 30.7 < μ < 32.9
**Use the given degree of confidence and sample data to construct a confidence interval for the population mean ****μ****. Assume that the population has a normal distribution.**
24) n = 30, = 88.7, s = 16.0, 90 percent
A) 82.73 < μ < 94.67 B) 83.74 < μ < 93.66 C) 83.77 < μ < 93.63 D) 80.65 < μ < 96.75
**Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.**
25) n = 144, x = 99; 90 percent
A) 0.623 < p < 0.753 B) 0.628 < p < 0.748 C) 0.627 < p < 0.749 D) 0.624 < p < 0.752
**Find the margin of error.**
26) 95% confidence interval; n = 21; = 0.64; s = 0.64
A) 0.135 B) 0.169 C) 0.157 D) 0.141
**Solve the problem.**
27) A researcher wishes to construct a 95% confidence interval for a population mean. She selects a simple random sample of size from the population. The population is normally distributed and σ is unknown. When constructing the confidence interval, the researcher should use the t distribution; however, she incorrectly uses the normal distribution. Will the true confidence level of the resulting confidence interval be greater than 95%, smaller than 95%, or exactly 95%?
A) Greater than 95% B) Exactly 95% C) Smaller than 95%
**Use the confidence level and sample data to find a confidence interval for estimating the population ****μ****.**
28) Test scores: n = 94, = 74.2, σ = 7.1; 99 percent
A) 72.3 < μ < 76.1 B) 73.0 < μ < 75.4 C) 72.8 < μ < 75.6 D) 72.5 < μ < 75.9
**Use the given information to find the P-value.**
29) The test statistic in a left-tailed test is z = -1.83.
A) 0.4326 B) 0.0336 C) 0.0443 D) 0.4232
**Express the null hypothesis H**_{o}** and the alternative hypothesis H**_{A}** in symbolic form. Use the correct symbol (****μ****, p, ****σ**** )for the indicated parameter.**
30) A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard deviation different from the σ = 3.3 mg claimed by the manufacturer.
A) H_{o}: σ ≥ 3.3 mg B) H_{o}: σ ≤ 3.3 mg C) H_{o}: σ ≠ 3.3 mg D) H_{o}_{: }σ = 3.3 mg
H_{A}: σ < 3.3 mg H_{A}: σ > 3.3 mg H_{A}_{: }σ = 3.3 mg H_{A}: σ ≠ 3.3 mg
**Use the given information to find the P-value.**
31) The test statistic in a left-tailed test is z = -2.05.
A) 0.0202 B) 0.0453 C) 0.5000 D) 0.4798
**Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test.**
32) A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard deviation different from the claimed by the manufacturer. Identify the type II error for the test.
A) 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.
B) 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.
C) The error of rejecting the claim that the standard deviation is 3.3 mg when it really is 3.3 mg.
**Find the critical value or values of x**^{2 based on the given information.}
33) : σ = 8.0
n = 10
α = 0.01
A) 1.735, 23.589 B) 2.088, 21.666 C) 21.666 D) 23.209
**Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim.**
34) The principal of a middle school claims that test scores of the seventh-graders at his school vary less than the test scores of the seventh-graders at a neighboring school, which have variation described by σ = 14.7. 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 not sufficient evidence to support the claim that the standard deviation is greater than 14.7.
B) There is not sufficient evidence to support the claim that the standard deviation is less than 14.7.
C) There is sufficient evidence to support the claim that the standard deviation is greater than 14.7.
D) There is sufficient evidence to support the claim that the standard deviation is less than 14.7.
**Find the value of the test statistic z using z = ** ** .**
35) The claim is that the proportion of drowning deaths of children attributable to beaches is more than 0.25, and the sample statistics include drowning deaths of children with 30% of them attributable to beaches.
A) 2.73 B) 2.89 C) -2.73 D) -2.89
**Find the appropriate p-value to test the null hypothesis, H**_{0: p1 = p2, using a significance level of 0.05.}
36) n_{1} = 50 n_{2} = 50
x_{1} = 3 x_{2} = 7
A) .0613 B) .0072 C) .1824 D) .1201
**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.**
37) We wish to compare the means of two populations using paired observations. Suppose that S_{d = 2.911, and n = 8, and that you wish to test the following hypothesis at the }1_{ percent level of significance:}
_{ H0: }_{μ}_{d = 0 against H1: }_{μ}_{d > 0.}
_{What decision rule would you use?}
A) Reject H_{0 if test statistic is less than }2.998_{.}
B) Reject H_{0 if test statistic is greater than }-2.998_{ and less than }2.998_{.}
C) Reject H_{0 if test statistic is greater than }-2.998_{.}
D) Reject H_{0 if test statistic is greater than }2.998_{.}
**Compute the test statistic used to test the null hypothesis that p**_{1 = p2.}
38) A report on the nightly news broadcast stated that 14 out of 123 households with pet dogs were burglarized and 24 out of 196 without pet dogs were burglarized.
A) -0.232 B) -0.093 C) -0.394 D) 0.000
**Construct the indicated confidence interval for the difference between population proportions p**_{1 - p2. Assume that the samples are independent and that they have been randomly selected.}
39) x_{1 = }20_{, n1 = }43_{ and x2 = }30_{, n2 = }56_{; Construct a 90% confidence interval for the difference between population proportions p1 - p2.}
A) -0.237 < - < 0.096 B) 0.267 < - < 0.663
C) 0.663 < - < 0.267 D) 0.299 < - < 0.631
**Solve the problem.**
40) Find the critical value corresponding to a sample size of 5 and a confidence level of 98 percent.
A) 0.484 B) 11.143 C) 13.277 D) 0.297
**Determine whether the given conditions justify using the margin of error E = ** **σ****/**** when finding a confidence interval estimate of the population mean ****μ****.**
41) The sample size is n = 5, σ = 12.7, and the original population is normally distributed.
A) Yes B) No
**Solve the problem.**
42) The confidence interval below for the population standard deviation is based on the following sample statistics: n = 41, = 42.3, and s = 5.6.
4.74 < σ < 6.88
What is the degree of confidence?
A) 95% B) 80% C) 99% D) 90%
**Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim.**
43) 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 sufficient evidence to support the claim that more than 62% of voters favor gun control.
B) There is sufficient evidence to warrant rejection of the claim that 62% of voters favor gun control.
C) There is not sufficient evidence to support the claim that 62% of voters favor gun control.
D) There is not sufficient evidence to warrant rejection of the claim that 62% of voters favor gun control.
44) A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz. 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 not sufficient evidence to warrant rejection of the claim that the mean weight is less than
B) There is sufficient evidence to warrant rejection of the claim that the mean weight is at least
C) There is sufficient evidence to warrant rejection of the claim that the mean weight is less than
D) There is not sufficient evidence to warrant rejection of the claim that the mean weight is at least
**Construct a confidence interval for ****μ**_{d, the mean of the differences d for the population of paired data. Assume that the population of paired differences is normally distributed.}
45) A test of writing ability is given to a random sample of students before and after they completed a formal writing course. The results are given below. Construct a 99% confidence interval for the mean difference between the before and after scores.
A) -0.5 < μ_{d} < 4.5 B) -0.2 < μ_{d} < 4.2 C) 1.2 < μ_{d} < 2.8 D) -0.1 < μ_{d} < 4.1
**Find the number of successes x suggested by the given statement.**
46) Among 870 people selected randomly from among the residents of one city, 21.61% were found to be living below the official poverty line.
A) 188 B) 193 C) 190 D) 186
**Use the confidence level and sample data to find a confidence interval for estimating the population ****μ****.**
47) A random sample of 78 light bulbs had a mean life of hours with a standard deviation of hours. Construct a 90 percent confidence interval for the mean life, μ, of all light bulbs of this type.
A) 399 < μ < 419 B) 398 < μ < 420 C) 402 < μ < 416 D) 401 < μ < 417
**Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test.**
48) Carter Motor Company claims that its new sedan, the Libra, will average better than 28 miles per gallon in the city. Identify the type I error for the test.
A) The error of failing to reject the claim that the mean is at most 28 miles per gallon when it is actually greater than 28 miles per gallon.
B) The error of rejecting the claim that the true proportion is more than 28 miles per gallon when it really is more than 28 miles per gallon.
C) The error of rejecting the claim that the mean is at most 28 miles per gallon when it really is at most 28 miles per gallon.
**Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is ****μ**_{d = 0. Compute the value of the t test statistic.}
49)
A) t = 2.890 B) t = 0.578 C) t = 0.415 D) t = 1.292
**Find the critical value or values of x**^{2 based on the given information.}
50) : σ > 26.1
n = 9
α = 0.01
A) 1.646 B) 20.090 C) 2.088 D) 21.666
1) Provided n > 30, s can be used in place of σ. If n ≤ 30, the population must be normal and σ must be known to use the formula.
2) The margin of error is the maximum likely difference between the observed sample mean and the true value for the population mean μ. The confidence interval is found by taking the sample mean and adding the margin of error E to find the high value and subtracting E to find the low value of the interval. In the interval the sample mean is 10.5 and the error estimate E is 0.85.
3) The sample proportion .
1) is unbiased (does not consistently overestimate or underestimate p).
2) is most consistent (has the least variation or all the measures of central tendency).
4) : p = 0.53. : p ≠ 0.53. Test statistic: z = -1.60. P-value: p = 0.0548.
Critical value: z = ±1.645. Fail to reject null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the actual percentage is 53%.
5) Test statistic: X^{2} = 38.786. Critical values: X^{2} = 16.791, 46.979. Fail to reject . There is not sufficient evidence to warrant rejection of the claim that blood pressure levels for women have the same variation as those for men.
6) Test statistic: t = 2.61. Critical value: t = 1.833. Reject . There is sufficient evidence to support the claim that the mean is greater than 520 hours.
7) Examples will vary.
8)
9) H_{0}: The proportions of absences are all the same.
H_{1}: The proportions of absences are not all the same.
Test statistic: χ^{2} = 28.308. Critical value: χ^{2} = 9.488. Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that absences occur on the different week days with the same frequency.
10) A point estimate is a single value used to approximate a population parameter. The sample mean is the best point estimate of μ.
11) : p = 0.5. : p < 0.5. Test statistic: z = -1.31. P-value: p = 0.0951.
Critical value: z = -1.645. Fail to reject null hypothesis. There is not sufficient evidence to warrant rejection of the claim that at least half of all voters prefer the Democrat.
12) H_{0}: p_{1} = p_{2}._{ }H_{1}: p_{1} > p_{2}.
Test statistic: z = 1.21 . Critical value: z = 1.645.
Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that the proportion of women favoring stricter gun control is higher than the proportion of men favoring stricter gun control.
13) : σ = 22 mmHg
: σ ≠ 22 mmHg
α = 0.05
Test statistic: = 32.89
0.1 < P-value < 0.2
Because the P-value is greater than the significance level of 0.05, we do not reject the null hypothesis. There is not sufficient evidence to reject the claim that
14) Test statistic t = 2.894. Critical values: t = ±2.262.
Reject H_{0}: μ_{d} = 0. There is sufficient evidence to warrant rejection of the claim that the mean is the same before and after viewing..
15) H_{0}: The proportions of occurrences are all equal.
H_{1}: Those proportions are not all equal.
Test statistic: χ^{2} = 8.263. Critical value: χ^{2} = 11.071. Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the characteristics occur with the same frequency.
16) H_{0}: The distribution of the sample agrees with the population distribution.
H_{1}: It does not agree.
Test statistic: χ^{2} = 31.938. Critical value: χ^{2} = 7.815. Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the distribution of the sample agrees with the distribution of the state populations.
17) H_{0}: Car color and being in an accident are independent.
H_{1}: Car color and being in an accident are dependent.
Test statistic: χ^{2} = 0.4287. Critical value: χ^{2} = 9.210.
Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that car color and being in an accident are independent.
18) H_{0}: Age and preferred music type are independent.
H_{1}: Age and preferred music type are dependent.
Test statistic: χ^{2} = 12.954. Critical value: χ^{2} = 9.488.
Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that age and preferred music type are independent.
19) H_{0}: The proportion of students smoking is the same at all four colleges.
H_{1}: The proportions are different.
Test statistic: χ^{2} = 17.832. Critical value: χ^{2} = 11.345.
Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the proportion of students smoking is the same at all four colleges.
20) Test statistic: t = 4.12. Critical values: t = ±2.145. Reject H_{0}: μ = 32.6. There is sufficient evidence to support the claim that the mean is different from 32.6.
21) D
22) C
23) D
24) B
25) D
26) C
27) C
28) A
29) B
30) D
31) A
32) A
33) A
34) D
35) B
36) C
37) D
38) A
39) A
40) C
41) A
42) D
43) D
44) B
45) A
46) A
47) C
48) C
49) D
50) B
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