AP STATS CHAPTER 9; SIGNIFICANCE TESTS FOR P

Consider a population with population proportion p, and a sample from the population with sample proportion p̂. Which of the following describes the purpose of the one-sample z-test?

• estimate p̂

• estimate p

• To estimate the probability of observing a value as extreme as p̂ given p

• To estimate the probability of observing a value as extreme as p given p̂

Tags

CCSS.HSS.IC.B.4

In a large mid-western university (the class of entering freshmen being on the order of 6000 or more students), an SRS of 100 entering freshmen found that 20 finished in the bottom third of their high school class. Admission standards at the university were tightened the following year. They took an SRS of 100 entering freshmen the following year and found that 10 finished in the bottom third of their high school class. Let p₁ and p₂ be the proportion of all entering freshmen in the two years who graduated in the bottom third of their high school class. What conclusion should we draw?

• We are 5% confident that the admissions standards have been tightened.

• Reject H₀ at the .01 significance level.

• Fail to reject H₀ at the .05 significance level.

• There is significant evidence, at the 5% level, of a decrease in the proportion of freshmen who graduated in the bottom third of their high school class that were admitted by the university.

• There is not significant evidence, at the 5% level, of a decrease in the proportion of freshmen who graduated in the bottom third of their high school class that were admitted by the university.

Tags

CCSS.HSS.IC.B.4

The germination rate is the rate at which plants begin to grow after the seed is planted. A seed company claims that the germination rate for their seeds is 90%. Concerned that the germination rate is actually less than 90%, a botanist obtained a random sample of seeds, of which only 80% germinated. What are the correct hypotheses for a one-sample z-test for a population proportion?

• H₀: p = 0.80

  H_A: p < 0.80

• H₀: p = 0.80

  H_A: p > 0.80

• H₀: p = 0.90

  H_A: p < 0.90

• H₀: p = 0.90

  H_A: p > 0.90

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: p̂ = 0.35

• H₀: p̂ = 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 n(p) 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 sampling distribution of the sample proportion 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 observations are independent.

In high school X, approximately 9 percent of the students saw a certain movie on opening night. From a random sample of 200 students from high school Y, 22 saw the movie on opening night. Consider a hypothesis test to investigate whether the proportion of all students in high school Y who saw the movie on opening night is greater than that of high school X. Which of the following is the standard deviation used to calculate the test statistic for the one-sample z-test?

A company that ships glass for a glass manufacturer claimed that its shipping boxes are constructed so that no more than 8 percent of the boxes arrive with broken glass. The glass manufacturer believed the actual percent is greater than 8 percent. The manufacturer selected a random sample of boxes and recorded the proportion of boxes that arrived with broken glass. The manufacturer tested the hypotheses H₀: p=0.08 versus Ha: p>0.08 at the significance level of α=0.01. The test yielded a p-value of 0.001. Assuming all conditions for inference were met, which of the following is the correct conclusion?

• The p-value is greater than α, and the null hypothesis is rejected. There is convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08.

• The p-value is greater than α, and the null hypothesis is not rejected. There is not convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08.

• The p-value is less than α, and the null hypothesis is rejected. There is convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08.

• The p-value is less than α, and the null hypothesis is not rejected. There is not convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08.

A significance test was performed to test the null hypothesis Ho: p =0.5 verses the alternate hypothesis Ha: p > 0.5. The test statisitic is z = 1.40. Which of the following is the closest p-value for this test?

• .0808

• .1492

• .1616

• .2984

• .9192

Past studies indicate that about 60 percent of the trees in a forested region are classified as softwood. A botanist studying the region suspects that the proportion might be greater than 0.60. The botanist obtained a random sample of trees from the region and conducted a test of

H₀: p=0.6 versus Ha: p>0.6 The p-value of the test was 0.015. Which of the following is a correct interpretation of the p-value?

• If it is true that 60 percent of the trees in a forested region are classified as softwood, 0.015 is the probability of obtaining a sample proportion as large as or larger than the one obtained by the botanist.

• If it is true that 60 percent of the trees in a forested region are classified as softwood, 0.015 is the probability of obtaining a sample proportion as small as or smaller than the one obtained by the botanist.

• If it is not true that 60 percent of the trees in a forested region are classified as softwood, 0.015 is the probability of obtaining a sample proportion as large as or larger than the one obtained by the botanist.

• If it is not true that 60 percent of the trees in a forested region are classified as softwood, 0.015 is the probability of obtaining a population proportion greater than 0.6.

A significance test allows you to reject a hypothesis Ho in favor of an alternative Ha at the 1% level of significance. What can you say about significance at the 5% level?

• Ho can be rejected at the 5% level of significance.

• Ho can not be rejected at the 5% level of significance.

• Ho can be accepted at the 5% level of significance.

• Ha can be rejected at the 5% level of significance.

• Can not be determined without knowing the p-value.