Exam 10: Introduction to Hypothesis Testing

The ____________________ of a test is the probability of observing a test statistic at least as extreme as the one from your sample, given that H₀ is true.

The p-value is the probability that the null hypothesis is true.

If a hypothesis is not rejected at the 0.10 level of significance, it:

One way of expressing how well a test performs is to report its power--the probability of detecting a false null hypothesis.

If a hypothesis is rejected at the 0.025 level of significance, it:

In a one-tail test, the p-value is found to be equal to 0.054. If the test had been two-tail, then the p-value would have been 0.027.

Which of the following statements is not true?

The owner of a local Jazz Club has recently surveyed a random sample of n = 200 customers of the club. She would now like to determine whether or not the mean age of her customers is over 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. The appropriate hypotheses to test are:

Rechargeable Batteries: A researcher wants to study the average lifetime of a certain brand of rechargeable batteries (in hours). In testing the hypotheses, H₀: $\mu$ = 950 hours vs. H₁: $\mu$ $\neq$ 950 hours, a random sample of 25 rechargeable batteries is drawn from a normal population whose standard deviation is 200 hours. -Calculate $\beta$ , the probability of a Type II error when $\mu$ = 1000 and $\alpha$ = 0.10.

LSAT Scores: The Admissions officer for the graduate programs at the University of Pennsylvania believes that the average score on the LSAT exam at his university is significantly higher than the national average of 1,300. An accepted standard deviation for LSAT scores is 125. A random sample of 25 scores had an average of 1,375. -State the appropriate null and alternative hypotheses.

A social researcher claims that the average adult listens to the radio less than 26 hours per week. He collects data on 25 individuals' radio listening habits and finds that the mean number of hours that the 25 people spent listening to the radio was 22.4 hours. If the population standard deviation is known to be eight hours, can we conclude at the 1% significance level that he is right?

A two-tail test for the population mean $\mu$ produces a test-statistic z = 1.89. The p-value associated with the test is 0.0588.

Rechargeable Batteries: A researcher wants to study the average lifetime of a certain brand of rechargeable batteries (in hours). In testing the hypotheses, H₀: $\mu$ = 950 hours vs. H₁: $\mu$ $\neq$ 950 hours, a random sample of 25 rechargeable batteries is drawn from a normal population whose standard deviation is 200 hours. -Recalculate $\beta$ if $\alpha$ is lowered from 0.10 to 0.05.

Explain the difference between accepting H₀ and failing to reject H₀.

For a two-tail test, the null hypothesis will be rejected at the 0.05 level of significance if the value of the standardized test statistic z is:

For a given sample size n, if the level of significance $\alpha$ is decreased, the power of the test will:

Rechargeable Batteries: A researcher wants to study the average lifetime of a certain brand of rechargeable batteries (in hours). In testing the hypotheses, H₀: $\mu$ = 950 hours vs. H₁: $\mu$ $\neq$ 950 hours, a random sample of 25 rechargeable batteries is drawn from a normal population whose standard deviation is 200 hours. -Interpret the meaning of the power of the test.

The power of the test refers to the probability of rejecting a false null hypothesis.

In a criminal trial, a Type II error is made when an innocent person is acquitted.

If we do not reject the null hypothesis, we conclude that there is enough statistical evidence to infer that the null hypothesis is true.