BackExact Method For each of the three different methods of hypothesis testing (identified in the left column), enter the P-values corresponding to the given alternative hypothesis and sample data. Use a 0.05 significance level. Note that the entries in the last column correspond to the Chapter Problem. How do the results agree with the large sample size?
Hypothesis Testing Using Rejection Regions In Exercises 7–12, (a) identify the claim and state H0 and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic z, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.
Changing Jobs A researcher claims that 40% of U.S. adults would consider changing jobs. In a random sample of 50 U.S. adults, 25 say they would consider changing jobs. At α=0.10, is there enough evidence to reject the researcher’s claim?
Hypothesis Testing Using Rejection Regions In Exercises 7–12, (a) identify the claim and state H0 and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic z, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.
Vaccinations In 2021, a reporter claims that at least 55% of U.S. adults feel that COVID-19 vaccinations should be required for high school students to attend school in the fall. In a random sample of 200 U.S. adults, 56% feel that COVID-19 vaccinations should be required for high school students to attend school in the fall. At α=0.10, is there enough evidence to reject the reporter’s claim?
Using Confidence Intervals to Test Hypotheses When analyzing the last digits of telephone numbers in Port Jefferson, it is found that among 1000 randomly selected digits, 119 are zeros. If the digits are randomly selected, the proportion of zeros should be 0.1.
d. Compare the results from the critical value method, the P-value method, and the confidence interval method. Do they all lead to the same conclusion?
"Blind Emotion [See Problem 11 in Section 10.2A.] When the area of the brain responsible for vision is destroyed, individuals experience cortical blindness. Patients with cortical blindness are unaware of any visual stimulus including light. In a 52-year-old male patient with cortical blindness (as a result of two strokes within a 38-day timeframe), a series of visual stimuli were presented on a computer screen. The patient was given two choices for each stimulus and asked to report what was on the screen. The patient’s responses were recorded by an individual who could not see the contents on the screen.
a. An initial baseline test was conducted by presenting black squares and circles on the white background of the screen. The patient correctly “guessed” the item on the screen in 90 of the 200 trials. Researchers concluded the patient’s performance was not statistically different from chance. Explain what this means using the language of hypothesis testing.
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"Living Alone? In 2000, 58% of females aged 15 or older lived alone, according to the U.S. Census Bureau. A sociologist tests whether this percentage is different today by conducting a random sample of 500 females aged 15 and older and finds that 285 are living alone. Is there sufficient evidence to conclude the proportion has changed since 2000?
b. What is the goal of the research?"
In Exercises 3–6, determine whether a normal sampling distribution can be used. If it can be used, test the claim.
Claim: p <0.12, α=0.01. Sample statistics: p_hat = 0.10, n=40
Small Sample Hypothesis Test: Super Bowl InvestingFrom Super Bowl I (1967) through Super Bowl XXXI (1997), the stock market increased if an NFL team won the Super Bowl and decreased if an AFL team won. This condition held 28 out of 31 years.
b. Use the binomial probability distribution to determine the P-value for the hypothesis test from part (a).
Feeling Your Age A research organization conducts a survey by randomly selecting adults and asking each, “How do you feel relative to your age?” The results are shown in the figure. (Adapted from Pew Research Center)
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a. Use a sign test to test the null hypothesis that the proportion of adults who feel older is equal to the proportion of adults who feel younger. Assign a + sign to each adult who responded “older,” assign a - sign to each adult who responded “younger,” and assign a 0 to each adult who responded “my age.” Use α = 0.05
In Exercises 3–6, determine whether a normal sampling distribution can be used. If it can be used, test the claim.
Claim: p > 0.70, α=0.04. Sample statistics: p_hat = 0.64, n=225
Statistics in the Media A headline read, “More Than Half of Americans Say Federal Taxes Too High.” The headline was based on a random sample of 1026 adult Americans in which 534 stated the amount of federal tax they have to pay is too high. Is this an accurate headline?
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”
Contacting Parents A research organization conducts a survey by randomly selecting adults and asking each, “How frequently do you contact your parents by phone?” The results are shown in the figure. (Adapted from Pew Research Center)
a. Use a sign test to test the null hypothesis that the proportion of adults who contact their parents by phone weekly is equal to the proportion of adults who contact their parents by phone daily. Assign a + sign to each adult who responded “weekly,” assign a - sign to each adult who responded “daily,” and assign a 0 to each adult who responded “other.” Use α = 0.05
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?
Hypothesis Testing Using Rejection Regions In Exercises 7–12, (a) identify the claim and state H0 and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic z, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.
Nursing A patient care manager claims that more than half of all nurses feel they became better professionals during the coronavirus pandemic. In a random sample of 300 nurses, 174 say they became better professionals during the pandemic. At α=0.01, is there enough evidence to support the manager’s claim?