Ch. 9/10.2 Quick Review Warm Up
Quiz by Katharine Semple
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- Q 1/15Score 0
Animal researchers studying cows and horses conducted a two-sample t-test for a difference in means to investigate whether grazing cows eat more grass, on average, than grazing horses. All conditions for inference were met, and the test produced a test statistic of t=1.664 and a p-value of 0.0487.
Which of the following is a correct interpretation of the p-value?
29Assuming that the mean amount of grass eaten by cows is greater than the mean amount of grass eaten by horses, the probability of observing a test statistic of at most 1.664 is 0.0487.
Assuming that the mean amount of grass eaten by cows is equal to the mean amount of grass eaten by horses, the probability of observing a test statistic of at most 1.664 is 0.0487.
The probability that cows eat more grass than horses, on average, is 0.0487.
Assuming that the mean amount of grass eaten by cows is equal to the mean amount of grass eaten by horses, the probability of observing a test statistic of at least 1.664 is 0.0487.
- Q1
Animal researchers studying cows and horses conducted a two-sample t-test for a difference in means to investigate whether grazing cows eat more grass, on average, than grazing horses. All conditions for inference were met, and the test produced a test statistic of t=1.664 and a p-value of 0.0487.
Which of the following is a correct interpretation of the p-value?
Assuming that the mean amount of grass eaten by cows is greater than the mean amount of grass eaten by horses, the probability of observing a test statistic of at most 1.664 is 0.0487.
Assuming that the mean amount of grass eaten by cows is equal to the mean amount of grass eaten by horses, the probability of observing a test statistic of at most 1.664 is 0.0487.
The probability that cows eat more grass than horses, on average, is 0.0487.
Assuming that the mean amount of grass eaten by cows is equal to the mean amount of grass eaten by horses, the probability of observing a test statistic of at least 1.664 is 0.0487.
45s - Q2
To investigate whether there is a difference in opinion on a certain proposal between two voting districts, A and B, two independent random samples were taken. From district A, 35 of the 50 voters selected were in favor of the proposal, and from district B, 36 of the 60 voters selected were in favor of the proposal.
Which of the following is the test statistic for the appropriate test to investigate whether there is a difference in the proportion of voters who are in favor of the proposal between the two districts (district A minus district B)?
45s - Q3
A random sample of 49 medical doctors in LA showed that they worked an average of 53.1 hours/week with a standard deviation of 7.2 hours/week. If the California average is 60 hours/week, does this give evidence that the LA doctors work significantly less than the rest of California?
2-Sample t Test
1-Prop z Test
1-Sample t Test
1-Sample t Interval
45s - Q4
Which of the following gives the probability of making a Type I error?
The sample size
The power
The p-value
The significance level
45s - Q5
In 1975, a random sample of 1484 adult U.S. citizens was surveyed, and 193 strongly agreed with the statement, “People should take care of themselves”. Then in 1991, a survey of 1013 adult U.S. citizens showed that only 61 strongly agreed with the statement. Does this indicate that the proportion of U.S. adults who strongly agree with the given statement has dropped?
2-Sample t Test
2-Prop z Test
2-Prop z Interval
2-Sample t Interval
45s - Q6
We are about to test a hypothesis using data from a well-designed study. Which is true?
I. A large P-value would be strong evidence against the null hypothesis.
II. We can set a higher standard of proof by choosing α = 10% instead of 5%.
III. If we reduce the risk of committing a Type I error, then the risk of a Type II error will also decrease.
I and II only
II only
III only
None of these
60s - Q7
City health officials will conduct a two-sample t-test for a difference in means to investigate whether stray dogs in the city have more fleas, on average, than do stray cats. A random sample of 22 stray dogs had a mean of 120 fleas and a standard deviation of 20 fleas. A random sample of 15 stray cats had a mean of 100 fleas and a standard deviation of 30 fleas.
Assuming a null hypothesis of no difference, which of the following is a correct test statistic for the test?
45s - Q8
A fast-food restaurant claims that a small order of french fries contains 120 calories. A nutritionist is concerned that the true average calorie count is higher than that. The nutritionist randomly selects 35 small orders of french fries and determines their calories. The resulting sample mean is 155.6 calories, and the p-value for the hypothesis test is 0.00093.
Which of the following is a correct interpretation of the p-value?
If the population mean is 155.6 calories, the pp-value of 0.00093 is the probability of observing a sample mean of 120 calories or more.
If the population mean is 120 calories, the pp-value of 0.00093 is the probability of observing a sample mean of 155.6 calories or less.
If the population mean is 120 calories, the pp-value of 0.00093 is the probability of observing a sample mean of 155.6 calories or more, or a sample mean of 84.4 calories or less.
If the population mean is 120 calories, the pp-value of 0.00093 is the probability of observing a sample mean of 155.6 calories or more.
45s - Q9
With an alpha level of 5%, what is the power of a test against an alternative for which the probability of a Type II error is 3%?
The power cannot be determined from the given data.
97%
95%
5%
45s - Q10
What is the power of a test?
A strong force
The probability that we correctly reject a false null hypothesis.
To reject the null, when the null is true.
The probability that we correctly accept a true null hypothesis.
45s - Q11
You plan to perform a hypothesis test with a level of significance of 0.05. What is the effect on the probability of committing a Type I error if the sample size is increased?
The effect cannot be determined without knowing if a Type II error is committed
The probability of committing a Type I error increases
The probability of committing a Type I error decreases
The probability of committing a Type I error is unchanged
45s - Q12
An environmental scientist wants to test the null hypothesis that an antipollution device for cars is not effective. Under which of the following conditions would a Type 1 error be committed?
The scientist concludes that the antipollution device is effective when it actually is not.
The scientist concludes that the antipollution device is not effective when it actually is.
The scientist concludes that the antipollution device is not effective when it actually is not.
A type 1 error cannot be committed in this situation.
45s - Q13
After a tropical storm in a certain state, news reports indicated that 19 percent of households in the state lost power during the storm. A state engineer believes that estimate is too low. The engineer will collect data to perform a hypothesis test on the proportion of all households without power. Which of the following are the appropriate hypotheses for such a test?
45s - Q14
The plant manager of a company that makes pillows claims that only 8 percent of the pillows made have a stitching defect. The quality control director thought that the percent might be different from 8 percent and selected a random sample of pillows to test. The director tested the hypotheses H0:p=0.08 versus Ha:p≠0.08 at the significance level of α=0.05. The p-value of the test was 0.03. Assuming all conditions for inference were met, which of the following is the correct conclusion?
The p-value is less than α, and the null hypothesis is not rejected. There is not convincing evidence to suggest the true proportion of stitching defects is not 0.08.
The p-value is less than α, and the null hypothesis is not rejected. There is convincing evidence to suggest the true proportion of stitching defects is not 0.08.
The p-value is less than α, and the null hypothesis is rejected. There is convincing evidence to suggest the true proportion of stitching defects is less than 0.08.
The p-value is less than α, and the null hypothesis is rejected. There is convincing evidence to suggest the true proportion of stitching defects is not 0.08.
45s - Q15
Polydactyl cats are cats with extra toes. A researcher believes that the proportion of the population of polydactyl cats in region A is greater than the proportion in region B. Let pB represent the population proportion of polydactyl cats in region A, and let pB represent the population proportion of polydactyl cats in region B. Which of the following are the appropriate hypotheses to test the researchers belief?
45s
