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1) Determine whether the given conditions justify using the margin of error E = z/2 / when finding a confidence interval estimate of the population mean .
The sample size is n = 8 and is not known.
Answers:
Yes
No
2) Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim.
A psychologist claims that more than 55 percent of the population suffers from professional problems due to extreme shyness. 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.
Answers:
A) There is not sufficient evidence to support the claim that the true proportion is less than 55 percent.
B) There is sufficient evidence to support the claim that the true proportion is greater than 55 percent.
C) There is not sufficient evidence to support the claim that the true proportion is greater than 55 percent.
D) There is sufficient evidence to support the claim that the true proportion is less than 55 percent.
3) Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol for the indicated parameter.
A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz.
Answers:
A) H0: = 14
H1: < 14
B) H0: > 14
H1: 14
C) H0: < 14
H1: 14
D) H0: = 14
H1: > 14
4) 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.
90% confidence; the sample size is 1580, of which 40% are successes
Answers:
A) 0.0203
B) 0.0242
C) 0.0158
D) 0.0253
5) 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.
95% confidence; the sample size is 3400, of which 20% are successes
Answers:
A) 0.0154
B) 0.0134
C) 0.0101
D) 0.0176
6)Provide an appropriate response.
Suppose that you wish to test a claim about a population mean. Which distribution should be used given that the sample is a simple random sample, is unknown, n = 15, and the population is not normally distributed?
Answers:
A) Neither the normal nor the t-distribution
B) t-distribution
C) Normal distribution
7) Use the given data to find the minimum sample size required to estimate the population proportion.
Answers:
A) 2
B) 27
C) 24
D) 81
8) 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.
95% confidence; n = 2342, x = 1353
Answers:
A) 0.0270
B) 0.0170
C) 0.0200
D) 0.0224
9) Use the given information to find the minimum sample size required to estimate an unknown population mean .
How many women must be randomly selected to estimate the mean weight of women in one age group. We want 90% confidence that the sample mean is within 3.3 lb of the population mean, and the population standard deviation is known to be 26 lb.
Answers:
A) 169
B) 239
C) 168
D)166
10) Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test.
A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO is less than 4 in a thousand. Identify the type I error for the test.
Answers:
A) Fail to reject the claim that the proportion of Americans that have seen a UFO is equal to 4 in a thousand when that proportion is actually greater than 4 in a thousand.
B) Reject the claim that the proportion of Americans that have seen a UFO is equal to 4 in a thousand when that proportion is actually 4 in a thousand.
C) Fail to reject the claim that the proportion of Americans that have seen a UFO is equal to 4 in a thousand when that proportion is actually less than 4 in a thousand.
D) Reject the claim that the proportion of Americans that have seen a UFO is equal to 4 in a thousand when that proportion is actually less than 4 in a thousand.
11) Use the given degree of confidence and sample data to construct a confidence interval for the population mean . Assume that the population has a normal distribution.
Thirty randomly selected students took the calculus final. If the sample mean was 77 and the standard deviation was 8.6, construct a 99% confidence interval for the mean score of all students.
Answers:
A) 72.69 < < 81.31
B) 72.67 < < 81.33
C) 74.33 < < 79.67
D) 73.13 < < 80.87
12) Use the confidence level and sample data to find the margin of error E. Round your answer to the same number of decimal places as the sample mean unless otherwise noted.
Systolic blood pressures for women aged 18-24: 94% confidence
A) 2.3 mm Hg
B) 2.6 mm Hg
C) 47.1 mm Hg
D) 2.2 mm Hg
13) Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test.
A consumer advocacy group claims that the mean mileage for the Carter Motor Company's new sedan is less than 30 miles per gallon. Identify the type I error for the test.
Answers:
A) Reject the claim that the mean is equal to 30 miles per gallon when it is actually less than 30 miles per gallon
B) Fail to reject the claim that the mean is equal to 30 miles per gallon when it is actually greater than 30 miles per gallon.
C) Fail to reject the claim that the mean is equal to 30 miles per gallon when it is actually less than 30 miles per gallon.
D) Reject the claim that the mean is equal to 30 miles per gallon when it is actually 30 miles per gallon.
14) 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).
The test statistic in a right-tailed test is z = 1.43.
Answers:
A) 0.0764; fail to reject the null hypothesis
B) 0.0764; reject the null hypothesis
C) 0.1528; fail to reject the null hypothesis
D) 0.1528; reject the null hypothesis
15) Use the confidence level and sample data to find a confidence interval for estimating the population . Round your answer to the same number of decimal places as the sample mean.
A random sample of 70 light bulbs had a mean life of hours with a standard deviation of Construct a 90% confidence interval for the mean life, , of all light bulbs of this type.
Answers:
A) 461 hr < < 481 hr
B) 460 hr < < 482 hr
C) 463 hr < < 479 hr
D) 464 hr < < 478 hr
16) Use the given information to find the minimum sample size required to estimate an unknown population mean .
How many business students must be randomly selected to estimate the mean monthly earnings of business students at one college? We want 95% confidence that the sample mean is within $131 of the population mean, and the population standard deviation is known to be $554.
Answers:
A) 69
B) 48
C) 97
D) 61
17) Use the confidence level and sample data to find the margin of error E. Round your answer to the same number of decimal places as the sample mean unless otherwise noted.
College students' annual earnings: 99% confidence;
Answers:
A) $258
B) $233
C) $891
D) $196
18) Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
When 314 college students are randomly selected and surveyed, it is found that 104 own a car. Find a 99% confidence interval for the true proportion of all college students who own a car.
Answers:
A) 0.263 < p < 0.400
B) 0.288 < p < 0.375
C) 0.269 < p < 0.393
D) 0.279 < p < 0.383
19) Solve the problem.
A one-sided confidence interval for p can be written as p < + E or p > - E where the margin of error E is modified by replacing z/2 with z. If a teacher wants to report that the fail rate on a test is at most x with 90% confidence, construct the appropriate one-sided confidence interval. Assume that a simple random sample of 68 students results in 8 who fail the test.
Answers:
A) p < 0.068
B) p < 0.182
C) p > 0.068
D) p < 0.168
20) Find the indicated critical z value.
Find the critical value z/2 that corresponds to a 91% confidence level.
Answers:
A) 1.645
B) 1.75
C) 1.70
D) 1.34
21) Solve the problem.
A simple random sample of women aged 18-24 is selected, and the systolic blood pressure of each woman is measured. The results (in mmHg) are as follows: = 120.4, s = 15.0. The sample size is less than 20. A 99% confidence interval for the population mean is found to be Find the sample size.
Answers:
A) 17
B) 14
C)15
D)16
22) Use the given degree of confidence and sample data to construct a confidence interval for the population mean . Assume that the population has a normal distribution.
The amounts (in ounces) of juice in eight randomly selected juice bottles are:
Construct a 98% confidence interval for the mean amount of juice in all such bottles.
Answers:
A) 15.89 oz < < 14.88 oz
B) 15.79 oz < < 14.98 oz
C) 14.98 oz < < 15.79 oz
D) 14.88 oz < < 15.89 oz
23) Provide an appropriate response.
Discuss the rationale for hypothesis testing. Refer to the comparison of the assumption and the sample results.
Answer:
24) identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim.
In a clinical study of an allergy drug, 108 of the 202 subjects reported experiencing significant relief from their symptoms. At the 0.01 significance level, test the claim that more than half of all those using the drug experience relief.
Answer:
25) Provide an appropriate response.
When determining the sample size for a desired margin of error, the formula is Based on this formula, discuss the fact that sample size is not dependent on the population size; that is, it is not necessary to sample a particular percent of the population.
