Exam 9: Hypothesis Testing

A university interested in tracking its honors program believes that the proportion of graduates with a GPA of 3.00 or below is less than 0.20. In a sample of 200 graduates, 30 students have a GPA of 3.00 or below. In testing the university's belief, the appropriate hypotheses are ________.

It is generally believed that no more than 0.50 of all babies in a town in Texas are born out of wedlock. A politician claims that the proportion of babies born out of wedlock is increasing. When testing the two hypotheses, H₀: p ≤ 0.50 and H_A: p > 0.50, p stands for ________.

If the p-value for a hypothesis test is 0.07 and the chosen level of significance is α = 0.05, then the correct conclusion is to ________.

It is generally believed that no more than 0.50 of all babies in a town in Texas are born out of wedlock. A politician claims that the proportion of babies born out of wedlock is increasing. In testing the politician's claim, how does one define the population parameter of interest?

Which of the following represents an appropriate set of hypotheses?

Which of the following are one-tailed tests?

The hypothesis statement H: µ = 25 is an example of a(an) ________ hypothesis.

Many cities around the United States are installing LED streetlights, in part to combat crime by improving visibility after dusk. An urban police department claims that the proportion of crimes committed after dusk will fall below the current level of 0.84 if LED streetlights are installed. Specify the null and alternative hypotheses to test the police department's claim.

For a given sample size, any attempt to reduce the likelihood of making one type of error (Type I or Type II) will increase the likelihood of the other error.

Massachusetts Institute of Technology grants pirate certificates to those students who successfully complete courses in archery, fencing, sailing, and pistol shooting ("MIT Awards Pirate Certificates to Undergraduates," Boston Globe, March 3). Sheila claims that those students who go on to earn pirate certificates are able to hit a higher proportion of bull's-eyes during the archery final exam than the course average of 0.15. Specify the null and alternative hypotheses to test her claim.

According to a Lawyers.com survey, only 35% of adult Americans had a will (The Wall Street Journal, December 12). Suppose a recent survey of 250 adult Americans found 100 adults with wills. A) Specify the competing hypotheses to determine whether the proportion of adult Americans who have a will differs from the proportion reported. B) Calculate the value of the test statistic and the p-value. C) At the 5% significance level, is the proportion different? Explain.

Consider the following hypotheses that relate to the medical field: H₀: A person is free of disease. H_A: A person has disease. In this instance, a Type II error is often referred to as ________.

When we reject the null hypothesis when it is actually false, we have committed ________.

Which of the following answers represents the objective of a hypothesis test?

A professional sports organization is going to implement a test for steroids. The test gives a positive reaction in 94% of the people who have taken the steroid. However, it erroneously gives a positive reaction in 4% of the people who have not taken the steroid. What is the probability of Type I and Type II errors giving the null hypothesis "the individual has not taken steroids."

When conducting a hypothesis test concerning the population mean, and the population standard deviation is unknown, the value of the test statistic is calculated as ________.

The Institute of Education Sciences measures the high school dropout rate as the percentage of 16-through 24-year-olds who are not enrolled in school and have not earned a high school credential. Last year, the high school dropout rate was 8.1%. A polling company recently took a survey of 1,000 people between the ages of 16 and 24 and found that 6.5% of them are high school dropouts. The polling company would like to determine whether the dropout rate has decreased. At a 5% significance level, the p-value and α are ________.

A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60. The population standard deviation is assumed to equal 0.40. The parameter to be tested is ________.

If the null hypothesis is rejected at a 1% significance level, then ________.

A Type I error occurs when we ________.