Hyp tests for props quiz

A researcher is conducting a study of charitable donations by surveying a simple random sample of households in a certain city. The researcher wants to determine whether there is convincing statistical evidence that more than 50 percent of households in the city gave a charitable donation in the past year. Let p represent the proportion of all households in the city that gave a charitable donation in the past year. Which of the following are appropriate hypotheses for the researcher?

• H₀: p = 0.5 and H_a: p > 0.5

• H₀: p = 0.5 and H_a: p ≠ 0.5

• H₀: p = 0.5 and H_a: p < 0.5

• H₀: p > 0.5 and H_a: p ≠ 0.5

• H₀: p > 0.5 and H_a: p = 0.5

Dan selected a random sample of 100 students from the 1,200 at his school to investigate preferences for making up school days lost due to emergency closings. The results are shown in the table below.

Dan incorrectly performed a large sample test of the difference in two proportions using 58/100 and 42/100 and calculated a p-value of 0.02. Consequently, he concluded that there was a significant difference in preference for the two options. Which of the following best describes his error in the analysis of these data?

• No statistical test was necessary because 0.58 is clearly larger than 0.42.

• The results of the test were invalid because less than 10% of the population was sampled.

• Dan performed a two-tailed test and should have performed a one-tailed test.

• A one-sample test for a proportion should have been performed because only one sample was used.

Tags

CCSS.HSS.IC.B.4

Approximately 38 percent of people living in Region W have the blood type O positive. A random sample of 100 people from Region X revealed that 35 people in the sample had the blood type O positive. Consider a hypothesis test to investigate whether the percent of people in Region X with O positive blood is different from that of in Region W. Which of the following is the appropriate null hypothesis for the investigation?

• H0: p-hat=0.35

• H0: p-hat=0.38

• H0: p=0.35

• H0: p=0.38

For a one-sample test for a population proportion p and sample size n, why is it necessary that np and n(1-p) are both at least 10 ?

• The sample size must be large enough to support an assumption that the distribution of the population is approximately normal.

• The sample size must be large enough to support an assumption that the distribution of the sample is approximately normal.

• The sample size must be large enough to support an assumption that the sampling distribution of the sample proportion is approximately normal.

• The sample size must be large enough to support an assumption that the observations are independent.

The p-value for a one-sided t-test is 0.10. If the test had been two-sided, what would the p-value have been?

• 0.05

• 0.20

• 0.90

• It depends on the direction of the alternative hypothesis.

An experimenter conducted a two-tailed hypothesis test on a set of data and obtained a p-value of 0.44. If the experimenter had conducted a one-tailed test on the same set of data, which of the following is true about the possible p-value(s) that the experimenter could have obtained?

• The only possible p-value is 0.22.

• The possible p-values are 0.22 and 0.78.

• The only possible p-value is 0.44.

• The possible p-values are 0.22 and 0.88.

A one-sample z-test for a population proportion was conducted to test H0:p=0.35 versus Ha:p≠0.35.

Assuming the conditions for inference were met, which combination of sample proportion and sample size would result in the smallest p-value of the test?

• p-hat=0.25 and n=100

• p-hat=0.40 and n=60

• p-hat= 0.25 and n=60

• p-hat=0.40 and n=100

A research organization reported that 41 percent of adults who were asked to describe their day responded that they were having a good day rather than a typical day or a bad day. To investigate whether the percent would be different for high school students, 600 high school students were randomly selected. When asked to describe their day, 245 students reported that they were having a good day rather than a typical day or a bad day. Do the data provide convincing statistical evidence that the proportion of all high school students who would respond that they were having a good day is different from 0.41 ?

• No, because the p-value is less than any reasonable significance level.

• No, because the p-value is greater than any reasonable significance level.

• Yes, because the p-value is less than any reasonable significance level.

• Yes, because the p-value is greater than any reasonable significance level.

Tags

CCSS.HSS.IC.B.4

A representative of a car manufacturer in the United States made the following claim in a news report.

"Ten years ago, only 53 percent of Americans owned American-made cars, but that figure is significantly higher today."

A research group conducted a study to investigate whether the claim was true. The group found that 56 percent of a randomly selected sample of car owners in the United States owned American-made cars. A test of the appropriate hypotheses resulted in a p-value of 0.283. Assuming the conditions for inference were met, is there sufficient evidence to conclude, at the significance level of a = 0.05, that the proportion of all car owners in the United States who own American-made cars has increased from what it was ten years ago?

• Yes, because 0.56 > 0.53.

• Yes, because a reasonable interval for the proportion is 0.56 ± 0.283.

• Yes, because 0.56 - 0.53 = 0.03 and 0.03 < 0.05.

• No, because 0.283 < 0.53.

• No, because 0.283 > 0.05.

Tags

CCSS.HSS.IC.B.4

A study reported that 14 percent of cars registered in 2015 had a manual transmission. An automotive researcher collected data on cars registered in 2021 to investigate whether the proportion of registered cars with a manual transmission is less than 0.14. The researcher took a random sample of 150 cars registered in 2021 and found 18 of the cars had a manual transmission.

After ensuring the conditions for inference were met, the researcher conducted an appropriate hypothesis test and calculated a p-value of 0.24. At the 5 percent level of significance, which of the following conclusions should be made?

• The null hypothesis should be rejected. There is significant evidence that the population proportion of registered cars with a manual transmission in 2021 is less than 0.14.

• The null hypothesis should be rejected. There is not significant evidence that the population proportion of registered cars with a manual transmission in 2021 is less than 0.14.

• The null hypothesis should not be rejected. There is significant evidence that the population proportion of registered cars with a manual transmission in 2021 is not less than 0.14.

• The null hypothesis should not be rejected. There is not significant evidence that the population proportion of registered cars with a manual transmission in 2021 is less than 0.14.

• The null hypothesis should not be rejected. There is significant evidence that the population proportion of registered cars with a manual transmission in 2021 is equal to 0.14.