Conditions for Tests/Intervals
Corey wants to use a one-sample z-interval to estimate the proportion of his coworkers who drink coffee every morning. He takes an SRS of 10 of his 50 total coworkers and finds that 6 of those sampled drink coffee every morning. Which conditions for constructing this confidence interval did Corey's sample meet? Choose all answers that apply:
A. The data is a random sample from the population of interest.
B. n(p-hat)≥10 and n(1-(p-hat)) ≥10
C. Individual observations can be considered independent.
A. The data is a random sample from the population of interest.
Given that the power of a significance test against a particular alternative is 96 percent, which of the following is true?
A. The probability of mistakenly rejecting a true null hypothesis is less than 4 percent
B. The probability of mistakenly rejecting a true null hypothesis is 4 percent
C. The probability of mistakenly rejecting a true null hypothesis is greater than 4 percent
D. The probability of mistakenly failing to reject a false null hypothesis is 4 percent
E. The probability of mistakenly failing to reject a false null hypothesis is different from 4 percent
D. The probability of mistakenly failing to reject a false null hypothesis is 4 percent
What is the critical value for a 96% confidence level?
A. 1.036
B. 1.645
C. 1.960
D. 2.054
E. 2.807
D. 2.054
A high school has six math teachers and six science teachers. When comparing their mean years of service, which of the following is most appropriate?
A. A two-sample z-test of population means
B. A two-sample t-test of population means
C. A one-sample z-test on a set of differences
D. A one-sample t-test on a set of differences
E. None of the above are appropriate
E. None of the above are appropriate
Which of the following is a true statement?
A. Tests of significance (hypothesis tests) are designed to measure the strength of evidence against the null hypothesis
B. A well-planned test of significance should result in a statement either that the null hypothesis is true or false
C. The null hypothesis is one-sided and expressed using < or > if there is interest in deviations in only one direction
D. When a true parameter value is farther from the hypothesized value, it becomes easier to reject the alternative hypothesis
E. Increasing the sample size makes it more difficult to conclude that an observed difference between observed and hypothesized values is significant
A. Tests of significance (hypothesis tests) are designed to measure the strength of evidence against the null hypothesis
A guidance counselor is interested in comparing GPAs of students with home access to the internet with students who do not have this access. She pulls the files of an SRS of ten students who do have home access to the Internet and an SRS of ten who do not, and proceeds to run a t-test to compare the mean GPAs of each group. Which of the following is a necessary assumption?
A. The population standard deviations from each group are known
B. The population standard deviations from each group are not known
C. The population standard deviations from each group are equal
D. The population of GPA scores from each group is normally distributed
E. The samples must be independent samples, and for each sample np and n(1-p) must both be at least 10.
D. The population of GPA scores from each group is normally distributed
What is the probability of a Type II error when a hypothesis test is being conducted at α=.05?
A. .05
B. .10
C. .90
D. .95
E. There is insufficient information to answer this question.
E. There is insufficient information to answer this question.
In general, how does doubling the sample size change the confidence interval size?
A. Doubles the interval size
B. Halves the interval size
C. Multiplies the interval size by 1.414
D. Divides the interval size by 1.414
E. This question cannot be answered without knowing the sample size
D. Divides the interval size by 1.414
In a one-sided hypothesis test for the mean, for a random sample of size 15 the t-score of the sample mean is 2.615. Is this significant at the 5 percent level? At the 1 percent level?
A. Significant at the 1 percent level but not at the 5 percent level
B. Significant at the 5 percent level but not at the 1 percent level
C. Significant at both the 1 percent level and the 5 percent level
D. Significant at neither the 1 percent level nor the 5 percent level
E. Cannot be determined from the given information
B. Significant at the 5 percent level but not at the 1 percent level
Which of the following is a true statement?
A. A P-value is a conditional probability
B. The P-value is the probability that the null hypothesis is true
C. A P-value is the probability the null hypothesis is true given a particular observed statistic
D. A P-value is the probability of Power
E. Large P-values are evidence against the null hypothesis because they say that the observed result is unlikely to occur when the null hypothesis is true
A. A P-value is a conditional probability
Nkechi wants to use a one-sample interval to estimate what proportion of candies in a bag are red. She takes a random sample of 24 of the 80 total candies and finds that 18 of the candies in the sample are red. Which conditions for constructing this confidence interval did Nkechi's sample meet? Choose all that apply:
A. The data is a random sample from the population of interest
B. The observed counts of successes and failures are both sufficiently large.
C. Individual observations can be considered independent.
A. The data is a random sample from the population of interest
Which of the following statements is incorrect?
A. The significance level of a test is the probability of a Type II error.
B. Given a particular alternative, the power of a test against that alternative is 1 minus the probability of the Type II error associated with that alternative.
C. If the significance level remains fixed, increasing the sample size will reduce the probability of a Type II error.
D. If the significance level remains fixed, increasing the sample size will raise the power.
E. Holding the sample size fixed, increasing the significance level will decrease the probability of a Type II error.
A. The significance level of a test is the probability of a Type II error.
(The significance level of a test is the probability of a Type I error, not Type II).
We are interested in the proportion p of people who drive pickup trucks in a large city. Seven percent of a simple random sample of 760 people say they drive pickups. What is the midpoint for a 99 percent confidence interval estimate of p?
A. .005
B. .495
C. .5
D. p
E. None of the above
E. None of the above
(The midpoint is .07)
An office manager believes that the percentage of employees arriving late is even greater than the previously claimed 7 percent. She conducts a hypothesis test on a random 200 employee arrivals and finds 23 punching in late. Is this strong evidence against the .07 claim?
A. Yes, because the P-value is .0062
B. Yes, because the P-value is 2.5
C. No, because the P-value is .0062
D. No, because the P-value is over .10
E. There is insufficient information to reach a conclusion.
A. Yes, because the P-value is .0062
A 2007 survey of 980 American drivers concluded that 38 percent of the driving population would be willing to pay higher gas prices to protect the environment. Which of the following best describes what is meant by the poll having a margin of error of 3 percent?
A. Three percent of those surveyed refused to participate in the poll
B. It would not be unexpected for 3 percent of the population to readily agree to the higher gas prices.
C. Between 343 and 402 of the 980 drivers surveyed responded that they would be willing to pay higher gas prices to protect the environment
D. If a similar survey of 980 American drivers was taken weekly, a 3 percent change in each week's results would not be unexpected
E. It is likely that between 35 and 41 percent of the driving population would be willing to pay higher gas prices to protect the environment
E. It is likely that between 35 and 41 percent of the driving population would be willing to pay higher gas prices to protect the environment
A market analyst is curious what proportion of Los Angeles residents have a landline telephone. A survey of 200 randomly selected Los Angeles residents shows that 48% of those selected have a landline telephone. The analyst wants to use this data to construct a one-sample z-interval for a proportion. Which conditions for constructing this confidence interval did their sample meet? Choose all answers that apply:
A. The data is a random sample from the population of interest.
B. The observed counts of successes and failures are both sufficiently large.
C. Individual observations can be considered independent.
All of the above
A company that produces paper towels continually monitors wet towel strength. If the mean strength from a sample drops below a specified level, the production process is halted, and the machinery inspected. Which of the following would result from a Type I error.
A. Halting the production process when sufficient customer complaints are received.
B. Halting the production process when the wet towel strength is below specifications.
C. Halting the production process when the wet towel strength is within specifications
D. Allowing the production process to continue when the wet towel strength is below specifications.
E. Allowing the production process to continue when the wet towel strength is within specifications.
C. Halting the production process when the wet towel strength is within specifications
A guidance counselor wishes to determine the mean number of changes in academic major by college students to within ± 0.1 at a 90% confidence level. What sample size should be chosen if it is known that the standard deviation is 0.45?
A. 8
B. 54
C. 55
D. 78
E. 110
C. 55
Suppose Hₒ: p = .6, Hₐ: p>.6, and against the alternative p =.7, the power is .8. Which of the following is a valid conclusion?
A. The probability of committing a Type I error is .1.
B. If p = .7 is true, the probability of failing to reject Hₒ is .2.
C. The probability of committing a Type II error is .3.
D. All of the above are valid conclusions.
E. None of the above are valid conclusions.
B. If p = .7 is true, the probability of failing to reject Hₒ is .2.
A confidence interval estimate is determined from the summer earnings of an SRS of n students. All other things being equal, which of the following will result in a smaller margin of error?
A. A greater confidence interval
B. A larger sample standard deviation
C. A larger sample size
D. Accepting less precision
E. Introducing bias into sampling
C. A larger sample size
A school administrator is curious what proportion of the 2,400 students at the school regularly eat breakfast. They take an SRS of 150 of these students, and 104 of them report that they regularly eat breakfast. The administrator wants to use this data to construct a one-sample z-interval for a proportion. Which conditions for constructing this confidence interval did their sample meet? Choose all answers that apply:
A. The data is a random sample from the population of interest.
B. The observed counts of successes and failures are both sufficiently large.
C. Individual observations can be considered independent.
All of the above
If all other variables remain constant, which of the following will not increase the power of a hypothesis test?
A. Increasing the sample size
B. Increasing the significance level
C. Increasing the probability of a Type II error
D. Decreased variability in the data
E. Increased distance between the true and hypothesized parameter
C. Increasing the probability of a Type II error
Changing from a 95 percent confidence interval estimate for a population proportion to a 99 percent confidence interval estimate, with all other thing being equal,
A. increases the interval size by 4 percent
B. decreases the interval size by 4 percent
C. increases the interval size by 31 percent
D. decreases the interval size by 31 percent
E. This question cannot be answered without knowing the sample size
C. increases the interval size by 31 percent
Using the same data, one student performs a test Hₒ: P = .85 with Hₐ: p ≠ .85; a second student performs a test Hₒ: P = .85 with Hₐ: p < .85. Even though both use the α = .05 level of significance, the first student claims there is not enough evidence to reject Hₒ, and the second student says there is enough evidence to reject Hₒ. Which of the following could have been the value for the test statistic?
A. z= -2.3
B. z= -1.8
C. z= -1.3
D. z= 1.3
E. z= 1.8
B. z= -1.8
A political action group wishes to learn the government approval rating on the environment. From a past study, they know that they will have to poll 270 people for their desired level of confidence. If they want to keep the same level of confidence but divide the margin of error in third, how many people will they have to poll?
A. 30
B. 90
C. 468
D. 810
E. 2,430
E. 2,430
(multiply sample size by a multiple of d2)