Exam 11: Introduction to Hypothesis Testing

In testing the hypotheses H₀: $\mu$ = 50 vs.H₁: $\mu$ < 50, we found that the standardized test statistic is z = -1.59.Calculate the p-value, and state your conclusion if $\alpha$ = .025.

The power of a test is measured by its capability of:

The critical values will bound the rejection and non-rejection regions for the null hypothesis.

To calculate the probability of a(n) ____________________ error you need to specify a value of $\mu$ other than the one given in the null hypothesis.

A Type I error is represented by $\alpha$ ; it is the probability of rejecting a true null hypothesis.

The probability of a Type I error is denoted by ____________________.

The probability of a test statistic falling in the rejection region is equal to the value of ____________________.

There are two approaches to making a decision in a hypothesis test once the test statistic has been calculated.One approach is the ____________________ method.The other approach is the p-value method.

Watching the News A researcher claims viewers spend an average of 40 minutes per day watching the news.You think the average is higher than that.In testing your hypotheses H₀: $\mu$ = 40 vs.H₁: $\mu$ > 40, the following information came from your random sample of viewers: = 42 minutes, n = 25.Assume $\sigma$ = 5.5, and $\alpha$ = 0.10. -{Watching the News Narrative} Calculate the value of the test statistic.

You cannot commit a(n) ____________________ error when the null hypothesis is true.

Reducing the probability of a Type I error also reduces the probability of a Type II error.

The operating characteristic curve plots the values of $\beta$ (the probability of committing a Type II error) versus the values of the population mean $\mu$ .

Suppose that 9 observations are drawn from a normal population whose standard deviation is 2.The observations are: 15, 9, 13, 11, 8, 12, 11, 7, and 10.At 95% confidence, you want to determine whether the mean of the population from which this sample was taken is significantly different from 10. a. State the null and alternative hypotheses. b. Compute the value of the test statistic. c. Compute the p-value. d. Interpret the results.

When a null hypothesis is rejected, the test is said to be statistically ____________________ at level $\alpha$ .

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

A Type I error is committed if we make:

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

If a marketer wishes to determine whether there is evidence that average family income in a community exceeds $32,000:

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. -{Rechargeable Batteries Narrative} Interpret the meaning of the power of the test.

Suppose an auto manufacturer states that their car goes from 0 to 60 miles per hour in 10 seconds on average, and you suspect that time is longer. a. Set up the null and alternative hypotheses to test this claim. b. Explain how you know which is the null hypothesis and which is the alternative hypothesis.