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Question
The general format for a confidence interval is:
A) point estimate z (standard deviation).
B) point estimate (critical value)(standard error).
C) margin of error (confidence coefficient) (standard error).
D) point estimate (critical value)(standard deviation)
Answer
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A major issue facing many states is whether to legalize casino gambling. Suppose the governor of one state believes that more than 55% of the state's registered voters would favor some form of legal casino gambling. However, before backing a proposal to allow such gambling, the governor has instructed his aides to conduct a statistical test on the issue. To do this, the aides have hired a consulting firm to survey a simple random sample of 300 voters in the state. Of these 300 voters, 175 actually favored legalized gambling.
Assuming that a significance level of 0.05 is used, what conclusion should the governor reach based on these sample data?
A) Since z = 1.1594 < 1.645, do not reject the null hypothesis.
The sample data do not provide sufficient evidence to conclude that more than 55 percent of the population favor legalized gambling.
B) Since z = 2.1316 > 1.645, reject the null hypothesis.
The sample data provide sufficient evidence to conclude that more than 55 percent of the population favor legalized gambling.
C) Since z = 1.1594 < 1.645, do not reject the null hypothesis.
The sample data do not provide sufficient evidence to conclude that more than 58 percent of the population favor legalized gambling.
D) Since z = 2.1316 > 1.645, reject the null hypothesis.
The sample data provide sufficient evidence to conclude that more than 58 percent of the population favor legalized gambling.
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At a recent meeting, the manager of a national call center for a major Internet bank made the statement that the average past-due amount for customers who have been called previously about their bills is now no larger than $20.00. Other bank managers at the meeting suggested that this statement may be in error and that it might be worthwhile to conduct a test to see if there is statistical support for the call center manager's statement. The file called Bank Call Center contains data for a random sample of 67 customers from the call center population. Assuming that the population standard deviation for past due amounts is known to be $60.00, what should be concluded based on the sample data? Test using α = 0.10.
A) Because p-value = 0.4121 > alpha = 0.10, we do not reject the null hypothesis.
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B) Because p-value = 0.4121 > alpha = 0.10, we reject the null hypothesis.
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The sample data provide sufficient evidence to reject the call center manager's statement that the mean past due amount is $20.00 or less.
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The director of a state agency believes that the average starting salary for clerical employees in the state is less than $30,000 per year. To test her hypothesis, she has collected a simple random sample of 100 starting clerical salaries from across the state and found that the sample mean is $29,750. Assuming the population standard deviation is known to be $2,500 and the significance level for the test is to be 0.05, what is the critical value (stated in dollars)?
A) For alpha = .05 and a one tailed, lower tail test, the critical value is z = -1.645. Solving for the critical x-bar: -1.645 = (x-bar - 30,000)/250, x-bar = $29,588.75
B) For alpha = .05 and a one tailed, lower tail test, the critical value is z = -1.96. Solving for the critical x-bar: -1.96 = (x-bar - 30,000)/250, x-bar = $34,211.14
C) For alpha = .05 and a one tailed, lower tail test, the critical value is z = -1.645. Solving for the critical x-bar: -1.645 = (x-bar - 30,000)/250, x-bar = $34,211.14
D) For alpha = .05 and a one tailed, lower tail test, the critical value is z = -1.96. Solving for the critical x-bar: -1.96 = (x-bar - 30,000)/250, x-bar = $30,411.25
Q:
For the following hypothesis:A) Because the computed value of t = 0.78 is not greater than 2.1727, reject the null hypothesis.B) Because the computed value of t = 0.78 is not greater than 2.1727, do not reject the null hypothesis.C) Because the computed value of t = 0.78 is not greater than 1.3277, reject the null hypothesis.D) Because the computed value of t = 0.78 is not greater than 1.3277, do not reject the null hypothesis.
Q:
For the following hypothesis:A) 1.58B) 0.78C) 1.14D) 0.41
Q:
For the following hypothesis test:A) Reject the null hypothesis if the calculated value of the test statistic, z, is greater than the critical value of the test statistic, 1.645. Otherwise, do not reject.B) Reject the null hypothesis if the calculated value of the test statistic, z, is greater than the critical value of the test statistic, 2.05. Otherwise, do not reject.C) Accept the null hypothesis if the calculated value of the test statistic, z, is greater than the critical value of the test statistic, 1.645. Otherwise, do not accept.D) Accept the null hypothesis if the calculated value of the test statistic, z, is greater than the critical value of the test statistic, 2.05. Otherwise, do not accept.
Q:
A contract calls for the mean diameter of a cylinder to be 1.50 inches. As a quality check, each day a random sample of n = 36 cylinders is selected and the diameters are measured. Assuming that the population standard deviation is thought to be 0.10 inch and that the test will be conducted using an alpha equal to 0.025, what would the probability of a Type II error be?
A) Approximately 0.1267
B) About 0.6789
C) 0.975
D) Can't be determined without knowing the "true" population mean.
Q:
When developing a confidence interval estimate, the confidence level is calculated based on the size of the sample and the population standard deviation.