Exam 9: One-Sample Hypothesis Tests

The null hypothesis is rejected when the p-value exceeds the level of significance.

For a given sample size, reducing the level of significance will decrease the probability of making a Type II error.

The researcher's null hypotheses is H₀: σ² ≤ 22. A sample of n = 25 items yields a sample variance of s² = 28.5. The test statistic is:

Guidelines for the Jolly Blue Giant Health Insurance Company say that the average hospitalization for a triple hernia operation should not exceed 30 hours. A diligent auditor studied records of 16 randomly chosen triple hernia operations at Hackmore Hospital, and found a mean hospital stay of 40 hours with a standard deviation of 20 hours. "Aha!" she cried, "the average stay exceeds the guideline." The p-value for a right-tailed test of her hypothesis is:

You are driving a van packed with camping gear (total weight 3,500 pounds including yourself and family) into a northern wilderness area. You take a "short cut" that turns into a one-lane road, with no room to turn around. After 11 miles you come to a narrow bridge with a faded sign saying, "Safe Up to 2 Tons." About a half-mile ahead, you can see that your road rejoins the main highway. You consider the sign's hypothesis carefully before making a decision. The cost of Type I error is:

When your sample size increases, the chance of both Type I and Type II error will increase.

A sample of 16 ATM transactions shows a mean transaction time of 67 seconds with a standard deviation of 12 seconds. Find the test statistic to decide whether the mean transaction time exceeds 60 seconds.

Increasing the sample size shifts the power curve upward, ceteris paribus.

The process that produces Sonora Bars (a type of candy) is intended to produce bars with a mean weight of 56 gm. The process standard deviation is known to be 0.77 gm. A random sample of 49 candy bars yields a mean weight of 55.82 gm. Which are the hypotheses to test whether the mean is smaller than it is supposed to be?

A smaller probability of Type II error implies higher power of the test.

For a right-tailed test of a hypothesis for a single population mean with n = 10, the value of the test statistic was t = 1.411. The p-value is:

In testing the hypotheses H₀: π ≤ π₀, H₁: π > π₀, we would use a right-tailed test.

In hypothesis testing, we are trying to reject the alternative hypothesis.

In testing a proportion, normality of p can be assumed if nπ₀ ≥ 10 and n(1 - π₀) ≥ 10.

After lowering the landing gear, the pilot notices that the "gear down and locked" light is not illuminated. "It's probably just a burned out light bulb," she says, as she proceeds on final approach for landing. Considering the pilot's hypothesis, which is the result of Type I error?

Which is not a likely reason to choose the z distribution for a hypothesis test of a mean?

"My careful physical examination shows no evidence of any serious problem," said Doctor Morpheus. "However, a very costly lab test can be performed to check for the rare condition known as estomalgia fatalis. The test is almost invariably negative for persons with your age and symptoms. My personal hypothesis is that the occasional stomach pain you reported is due to indigestion caused by eating tacos with too much hot sauce. But you must decide for yourself." As you consider your doctor's hypothesis, what would be the consequence of Type I error on your part?

Given a normal distribution with σ = 3, we want to test the hypothesis H₀: μ = 20. We find that the sample mean is 21. The test statistic is:

In a two-tailed test, a statistician got a z test statistic of 1.82. What is the p-value?

Given H₀: μ ≥ 18 and H₁: μ < 18, we would commit a Type I error if we: