WorksheetsAP Statistics Inference Tests and Intervals
Total questions: 15
Worksheet time: 15mins
I8: A survey of 1,000 Americans reveals that 525 believe that whales are an endangered animal and should have protection from the fishing industry. In a survey of 750 Japanese, 325 believe that whales are endangered and should be protected. To test at the 5% significance level whether or not the data are significant evidence that the proportion of Japanese who believe that whales need protection is less than the proportion of Americans with this believe, a students sets up the following: H0: p = 0.525 and Ha: p < 0.525, where p is the proportion of Japanese with this belief. Which of the following is a true statement?
The student has set up a correct hypothesis test.
Given the large sample sizes, a 1 percent significance level would be more appropriate.
A two-sided test would be more appropriate.
Given the pooled proportion is 0.486, Ha: p < 0.486 would be more appropriate.
A two-population difference in proportions hypothesis test would be more appropriate.
A fitness center advertises that the average pulse rate of its members is 68.4 bpm. A high school AP Stats instructor suspects this is a made-up number and runs a hypothesis test on an SRS of 48 members, calculating a mean of 71.0 bpm with a standard deviation of 10.3 bpm. In which of the following intervals is the P-value located?
p < 0.01
0.01 < p < 0.02
0.02 < p < 0.05
0.05 < p < 0.10
p > 0.10
I11: 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?
8
54
55
78
110
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% level? At the 1% level?
Significant at 1%, not at 5%
Significant at 5%, not at 1%
Significant at both
Significant at neither
There is not enough information to determine
I13: 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 greater confidence level
A larger sample standard deviation
A larger sample size
Accepting less precision
Introducing bias into sampling
Which of the following is a true statement?
Tests of significance (hypothesis tests) are designed to measure the strength of evidence against the null hypothesis.
A well-planned test of significance should result in a statement either that the null hypothesis is true or that it is false.
The null hypothesis is one-sided and expressed using either < or > if there is interest in deviations in only one direction.
When a true parameter value is farther from the hypothesized value, it becomes easier to reject the alternative hypothesis.
Increasing the sample size makes it more difficult to conclude that an observed difference between observed and hypothesized values is significant.
To test whether husbands or wives have greater manual agility, an SRS of 50 married couples is chosen, and all 100 people are given a 1-minute period to find a place strangely shaped pegs into matching holes. What is the conclusion at a 5% significance level if a two-sample hypothesis test: H0: u1 - u2 = 0, Ha: u1 - u2 ≠ 0, results in a p-value of 0.15
The observed difference between husbands and wives is significant.
The observed difference is not significant.
A conclusion is not possible without knowing the mean number of pegs placed by husbands and wives.
A conclusion is not possible without knowing both the mean and standard deviation of the number of pegs placed by husbands and by wives.
A two-sample hypothesis test should not be used in this example.
I20: An office manager believes that the percentage of employees arriving late is even greater than the previously claimed 7%. She conducts a hypothesis test on a random 200 employee arrivals and finds 23 punching in late. Is this strong evidence against the 0.07 claim?
Yes, p-value is 0.0062
Yes, p-value is 2.5
No, p-value is only 0.0062
No, p-value is over 0.10
There is insufficient information to reach a conclusion.
When making an inference about a population mean, which of the following suggests the use of z-scores rather than t-scores?
Outliers are absent.
The population is normal.
The sample size is under 30.
Strong skew is absent.
The population standard deviation is known.
A congressional representative serving on the Joint Committee on Taxation states that the average yearly charitable contributions for taxpayers is $1,250. A lobbyist for a national church organization who believes that the real figure is lower samples 12 families and comes up with a mean of $1,092 and a standard deviation of $308. Where is the p-value?
Below 0.01
Between 0.01 and 0.025
Between 0.025 and 0.05
Between 0.05 and 0.10
Over 0.10
Which of the following is a true statement?
The p-value of a test is the probability of obtaining a result as extreme as or more extreme than the one obtained, assuming the null hypothesis is true.
If the p-value for a test is 0.043, the probability that the null hypothesis is true is 0.043.
When the null hypothesis is rejected, it is because it is not true.
The greater the p-value, the greater the evidence against the null hypothesis.
A very large p-value provides convincing evidence that the null hypothesis is true.
In a random survey of 500 women, 315 said they would rather be poor and thin than rich and fat; in a random survey of 400 men, 220 said they would rather be poor and thin than rich and fat. Is there sufficient evidence to show that the proportion of women who would rather be poor and thin than rich and fat is greater than the proportion of men who would rather be poor and thin than rich and fat?
Because 0.63 > 0.55, there is strong evidence that the proportion of women is greater than that of men.
Because 0.0075 < 0.01, there is very strong evidence that the proportion of women is greater than that of men.
Because 0.01 < 0.0329 < 0.05 there is strong evidence that the proportion of women is greater than that of men.
There is insufficient evidence that the proportion of women is greater than that of men.
There is insufficient information to determine whether the proportion of women is greater than that of men.
Given an experiment with H0: μ = 25, Ha: μ > 25, and a possible true population value of 26, which of the following increase with an increase in the sample size n?
The probability of a Type I error
The probability of a Type II error
The power of the test
The significance level α
1 - power
I50: A researcher believes that a new diet should improve weight gain in laboratory mice. If the average gain for 12 mice on the new diet is 5.3 ounces with a standard deviation of 0.5 ounces, while 15 control mice on the old diet gain an average of 5 ounces with a standard deviation of 0.4 ounces, where is the p-value?
Below 0.01
Between 0.01 and 0.025
Between 0.025 and 0.05
Between 0.05 and 0.10
Over 0.10
The school superintendent wants to know what percentage of property owners are willing to support an increase in school taxes. What size sample should be obtained to determine with 90% confidence the support level to within 5%?
17
33
271
289
1,083
