BackEmergency 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.
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).
Suppose we are testing the hypothesis H0: p = 0.3 versus H1: p > 0.3 and we find the P-value to be 0.23. Explain what this means. Would you reject the null hypothesis? Why?
In Problems 1–6, test the hypothesis using the P-value approach. Be sure to verify the requirements of the test.
H₀: p = 0.3 versus H₁: p > 0.3
n = 200; x = 75; α = 0.05
You Explain It! Stock Analyst Throwing darts at the stock pages to decide which companies to invest in could be a successful stock-picking strategy. Suppose a researcher decides to test this theory and randomly chooses 100 companies to invest in. After 1 year, 48 of the companies were considered winners; that is, they outperformed other companies. To assess whether the dart-picking strategy resulted in a majority of winners, the researcher tested H₀: p = 0.5 versus H₁: p > 0.5 and obtained a P-value of 0.2743. Explain what this P-value means and write a conclusion for the researcher.
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.
c. The researchers wanted to determine if the patient could identify other facial characteristics. They randomly showed male or female faces and asked the patient to identify the gender. The patient was correct in 89 of 200 trials. What does this suggest?
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?
Ghosts The following table summarizes results from a Pew Research Center survey in which subjects were asked whether they had seen or been in the presence of a ghost. Use a 0.01 significance level to test the claim that gender is independent of response. Does the conclusion change if the significance level is changed to 0.05?
Sleeping Patterns of Pregnant Women A random sample of 150 pregnant women indicated that 81 napped at least twice per week. Do a majority of pregnant women nap at least twice a week? Use the α = 0.05 level of significance.
Source: National Sleep Foundation.
[NW] Government Waste Gallup News Service conducted a survey of 1017 American adolts aged 18 years or older. The respondents were asked, “Of every tax dollar that goes to the federal government in Washington, D.C., do you believe 51 cents or more are wasted?” Of the 1017 individuals surveyed, 35% indicated that 51 cents or more is wasted. Gallup reported that 35% of all adolt Americans 18 years or older believe the federal government wastes at least 51 cents of each dollar spent, with a margin of error of 4% and a 95% level of confidence.
What can be inferred from this survey?