Exam 9: Hypothesis Testing

The alternative hypothesis typically agrees with the status quo.

A newly hired basketball coach promised a high-paced attack that will put more points on the board than the team's previously tepid offense historically managed. After a few months, the team owner looks at the data to test the coach's claim. He takes a sample of 36 of the team's games under the new coach and finds that they scored an average of 101 points with a standard deviation of 6 points. Over the past 10 years, the team had averaged 99 points. What is the value of the appropriate test statistic to test the new coach's claim at the 1% significance level?

To obtain the p-value for a right-tailed test of the population mean, when σ is unknown, we use the Excel's function ________.

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 real estate investor thinks the real estate market has bottomed out. One of the variables he examined to arrive at this conclusion was the proportion of houses sold at or above the asking price. Last year, the proportion of houses sold at or above the asking price was 14%. The real estate investor takes a random sample of 40 recently sold houses and finds that nine of them are selling at or above the asking price. A) Specify the population parameter to be tested. B) Specify the null and alternative hypotheses to determine whether the proportion of houses sold at or above the asking price has increased. C) Calculate the value of the test statistic and the p-value. D) At the 10% significance level, can you conclude that the proportion of houses sold at or above the asking price has increased?

A schoolteacher is worried that the concentration of dangerous, cancer-causing radon gas in her classroom is greater than the safe level of 4pCi/L. The school samples the air for 36 days and finds an average concentration of 4.4pCi/L with a standard deviation of 1pCi/L. At a 5% significance level, the decision is to ________.

A university wants to know if the average salary of its graduates has increased since 2015. The average salary of graduates prior to 2015 was $48,000. Since 2015, the university surveyed 256 graduates and found an average salary of $48,750. Assume that the standard deviation of all graduates' salaries is $7,000. A) Specify the null and alternative hypotheses to determine whether the average salary of graduates has increased. B) Calculate the value of the test statistic and the p-value at a 5% significance level. C) At the 5% significance level, can you conclude that salaries have increased? Explain.

If the chosen significance level is α = 0.05, then ________.

If we reject a null hypothesis at the 1% significance level, then we have ________ evidence that the null hypothesis is false.

Given the ________ of the z distribution, the p-value for a two-tailed test is twice that of the p-value for a one-tailed test.

In a one-tailed test, the rejection region is located under one tail (left or right) of the corresponding probability distribution, while in a two-tailed test this region is located under both tails.

A Type II error is made when we reject the null hypothesis and the null hypothesis is actually false.

An engineer is designing an experiment to test if airplane engines are faulty and unsafe to fly. The engineer expects 0.0001% of engines to be unsafe. The null hypothesis is that the probability of an unsafe engine is less than or equal to 0.0001% and the alternative hypothesis is that the probability the engine is unsafe is greater than 0.0001%. A) Describe the consequences of Type I and Type II errors. B) Should the engineer design the test with a higher alpha or a higher beta? Explain.

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. The value of the test statistic and its associated p-value are ________.

A schoolteacher is worried that the concentration of dangerous, cancer-causing radon gas in her classroom is greater than the safe level of 4pCi/L. The school samples the air for 36 days and finds an average concentration of 4.4pCi/L with a standard deviation of 1pCi/L. To test whether the average level of radon gas is greater than the safe level, 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. Identify the correct null and alternative hypotheses to test the politician's claim.

When conducting a hypothesis test for a given sample size, if the probability of a Type I error decreases, then the ________.

Vermont-based Green Mountain Coffee Roasters dominates the market for single-serve coffee in the United States, with its subsidiary Keurig accounting for approximately 70% of sales ("Rivals Try to Loosen Keurig's Grip on Single-Serve Coffee Market," Chicago Tribune, February 26). But Keurig's patent on K-cups, the plastic pods used to brew the coffee, is expected to expire this year, allowing other companies to better compete. Suppose a potential competitor has been conducting blind taste tests on its blend and finds that 47% of consumers strongly prefer its French Roast to that of Green Mountain Coffee Roasters. After tweaking its recipe, the competitor conducts a test with 144 tasters, of which 72 prefer its blend. The competitor claims that its new blend is preferred by more than 47% of consumers to Green Mountain Coffee Roasters' French Roast. What is the value of the appropriate test statistic to test this claim?

When conducting a hypothesis test for a given sample size, if α is increased from 0.05 to 0.10, then ________.

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. To establish whether the mean GPA exceeds 3.50, the appropriate hypotheses are ________.