Exam 9: Hypothesis Testing

A Type II error occurs when we ________.

What is the decision rule when using the p-value approach to hypothesis testing?

A Massachusetts state police officer measured the speed of 100 motorists on the Massachusetts Turnpike and found that 70 exceeded the posted speed limit by more than 10 miles per hour. The police officer claims that more than 60% of motorists drive at least 10 miles per hour more than the posted speed on the turnpike. A) Specify the null and alternative hypotheses to test the officer's claim. B) Calculate the value of the test statistic. C) At the 5% significance level, what is the p-value to test the officer's claim? D) At the 5% significance level, does the evidence support the officer's claim?

Billy wants to test whether the average speed of his favorite pitcher's fastball differs from the league average of 92 miles per hour. He takes a sample of 36 of the pitcher's fastballs and computes a sample mean of 94 miles per hour. Assume that the standard deviation of the population is 4 miles per hour. A) Specify the null and alternative hypotheses to test Billy's claim. B) Calculate the value of the test statistic and the p-value. C) At the 5% significance level, can you conclude that Billy's favorite pitcher's fastball differs in speed from the league average? D) At the 1% significance level, can you conclude that Billy's favorite pitcher's fastball differs in speed from the league average?

A car dealer who sells only late-model luxury cars recently hired a new salesperson and believes that this salesperson is selling at lower markups. He knows that the long-run average markup in his lot is $5,600. He takes a random sample of 16 of the new salesperson's sales and finds an average markup of $5,000 and a standard deviation of $800. Assume the markups are normally distributed. What is the value of an appropriate test statistic for the car dealer to use to test his claim?

Consider the following competing hypotheses: H₀: μ = 0, H_A: μ ≠ 0. The value of the test statistic is z = −1.38. If we choose a 5% significance level, then we ________.

We define the allowed probability of making a Type I error as α, and we refer to 100α% as the ________.

To test if the mean IQ of employees in an organization is greater than 100, a sample of 30 employees is taken and the value of the test statistic is computed as t₂₉ = 2.42 If we choose a 5% significance level, we ________.

A hypothesis test regarding the population mean is based on ________.

A statistics professor works tirelessly to catch students cheating on his exams. He has particular routes for his teaching assistants to patrol, an elevated chair to ensure an unobstructed view of all students, and even a video recording of the exam in case additional evidence needs to be collected. He estimates that he catches 95% of students who cheat in his class, but 1% of the time that he accuses a student of cheating he is actually incorrect. Consider the null hypothesis, "the student is not cheating." What is the probability of a Type I error?

A fast-food franchise is considering building a restaurant at a busy intersection. A financial advisor determines that the site is acceptable only if, on average, more than 300 automobiles pass the location per hour. The advisor tests the following hypotheses: H₀: μ ≤ 300. H_A: μ > 300. The consequences of committing a Type I error would be that ________.

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, how does one define the population parameter of interest?

The Department of Education would like to test the hypothesis that the average debt load of graduating students with a bachelor's degree is equal to $17,000. A random sample of 34 students had an average debt load of $18,200. It is believed that the population standard deviation for student debt load is $4,200. The α is set to 0.05. The p-value for this hypothesis test would be ________.

A fast-food franchise is considering building a restaurant at a busy intersection. A financial advisor determines that the site is acceptable only if, on average, more than 300 automobiles pass the location per hour. The advisor tests the following hypotheses: H₀: μ ≤ 300. H_A: μ > 300. The consequences of committing a Type II error would be that ________.

The alternative hypothesis typically ________.

Which of the following types of tests may be performed?