9. Hypothesis Testing for One Sample

Randomization: Testing a Claim About a Proportion

In Exercises 5–8, use the randomization procedure for the indicated exercise.

Section 8-2, Exercise 9 “Cursed Movie”

Job Search A Gallup poll of 195,600 employees showed that 51% of them were actively searching for new jobs. Use a 0.01 significance level to test the claim that the majority of employees are searching for new jobs

Perception and Reality In a presidential election, 308 out of 611 voters surveyed said that they voted for the candidate who won (based on data from ICR Survey Research Group). Use a 0.05 significance level to test the claim that among all voters, the percentage who believe that they voted for the winning candidate is equal to 43%, which is the actual percentage of votes for the winning candidate. What does the result suggest about voter perceptions?

Lightning Deaths The graph in Cumulative Review Exercise 5 was created by using data consisting of 242 male deaths from lightning strikes and 64 female deaths from lightning strikes. Assume that these data are randomly selected lightning deaths and proceed to test the claim that the proportion of male deaths is greater than . Use a 0.01 significance level. Any explanation for the result?

In Exercises 1–10, based on the nature of the given data, do the following:

a. Pose a key question that is relevant to the given data.

b. Identify a procedure or tool from this chapter or the preceding chapters to address the key question from part (a).

c. Analyze the data and state a conclusion.

Video Games In a survey of subjects aged 18–29, subjects were asked if they play video games often or sometimes. Among 984 females, 49% answered “yes” (based on data from a Pew Research Center survey).

"Spanking

In March 1995, The Harris Poll reported that 80% of parents spank their children. Suppose a recent poll of 1030 adult Americans with children finds that 781 indicated that they spank their children. If we assume parents’ attitude toward spanking has not changed since 1995, how many of 1030 parents surveyed would we expect to spank?

Do the results of the survey suggest that parents’ attitude toward spanking may have changed since 1995? Why?"

Self-InjuryAccording to the article “Self-injurious Behaviors in a College Population,” 17% of undergraduate or graduate students have had at least one incidence of self-injurious behavior. The researchers conducted a survey of 40 college students who reported a history of emotional abuse and found that 12 of them have had at least one incidence of self-injurious behavior. What do the results of this survey tell you about college students who report a history of emotional abuse?

Taught Enough Math? In 1994, 52% of parents with children in high school felt it was a serious problem that high school students were not being taught enough math and science. A recent survey found that 256 of 800 parents with children in high school felt it was a serious problem that high school students were not being taught enough math and science. Do parents feel differently today than they did in 1994? Use the α = 0.05 level of significance?

Sneeze According to work done by Nick Wilson of Otago University Wellington, the proportion of individuals who cover their mouth when sneezing is 0.733. As part of a school project, Mary decides to confirm this by observing 100 randomly selected individuals sneeze and finds that 78 covered their mouth when sneezing.

a. What are the null and alternative hypotheses for Mary’s project?

b. Verify the requirements that allow use of the normal model to test the hypotheses are satisfied.

c. Does the sample evidence contradict Professor Wilson’s findings?

Emergency Room The proportion of patients who visit the emergency room (ER) and die within the year is 0.05. Source: SuperFreakonomics. Suppose a hospital administrator is concerned that his ER has a higher proportion of patients who die within the year. In a random sample of 250 patients who have visited the ER in the past year, 17 have died. Should the administrator be concerned?

Teen Prayer In 1995, 40% of adolescents stated they prayed daily. A researcher wants to know whether this percentage has become higher since then. He surveys 40 adolescents and finds that 18 pray on a daily basis. Is there enough evidence to support the proportion of adolescents who pray daily has increased at the α = 0.05 level of significance?

Course RedesignPass rates for Intermediate Algebra at a community college are 52.6%. In an effort to improve pass rates in the course, faculty of a community college develop a mastery-based learning model where course content is delivered in a lab through a computer program. The instructor serves as a learning mentor for the students. Of the 480 students who enroll in the mastery-based course, 267 pass.

b. At the 0.01 level of significance, decide whether the sample evidence suggests the mastery-based learning model improved pass rates.

In Problems 7–12, test the hypothesis using (a) the classical approach and (b) the P-value approach. Be sure to verify the requirements of the test.

H0: p = 0.3versusH1: p > 0.3n = 200;x = 75;α = 0.05

In Problems 7–12, test the hypothesis using (a) the classical approach and (b) the P-value approach. Be sure to verify the requirements of the test.

H0: p = 0.4versusH1: p ≠ 0.4n = 1000;x = 420;α = 0.01

You Explain It! ESPSuppose an acquaintance claims to have the ability to determine the birth month of randomly selected individuals. To test such a claim, you randomly select 80 individuals and ask the acquaintance to state the birth month of the individual. If the individual has the ability to determine birth month, then the proportion of correct birth months should exceed 1/12 ≈ 0.083, the rate one would expect from simply guessing.

b. Suppose the individual was able to guess nine correct birth months. The P-value for such results is 0.1726. Explain what this P-value means and write a conclusion for the test.