Exam 11: Introduction to Hypothesis Testing

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

In a two-tail test for the population mean, the null hypothesis will be rejected at $\alpha$ level of significance if the value of the standardized test statistic z is such that:

NARRBEGIN: Rechargeable Batteries 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: $\mu$ =950 hours, a random sample of 25 rechargeable batteries is drawn from a normal population whose standard deviation is 200 hours.NARREND -{Rechargeable Batteries Narrative} Review the results of the previous questions. What is the effect of decreasing the significance level on the value on $\beta$ ?

A Type I error is committed if we make:

NARRBEGIN: Production Filling Production Filling A production filling operation has a historical standard deviation of 6 ounces. When in proper adjustment, the mean filling weight for the production process is 50 ounces. A quality control inspector periodically selects at random 36 containers and uses the sample mean filling weight to see if the process is in proper adjustment.NARREND -{Production Filling Narrative} Using a standardized test statistic, test the hypothesis at the 5% level of significance if the sample mean filling weight is 48.6 ounces.

In testing the hypothesis H₀: $\mu$ = 100 vs. H₁: $\mu$ > 100, the p-value is found to be 0.074, and the sample mean is 105. Which of the following statements is true?

The level of significance can be:

Using the confidence interval when conducting a two-tail test for the population mean $\mu$ , we do not reject the null hypothesis if the hypothesized value for $\mu$ falls between the lower and upper confidence limits.

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

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.

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.

The power of a test plus the probability of a Type II error equals ____________________.

The numerical quantity computed from the data that is used in deciding whether to reject H₀ is the:

If a null hypothesis is rejected at the 0.05 level of significance, it must be rejected at the 0.025 level.

As the sample size increases, the operating characteristic curves drop down to zero at a(n) ____________________ rate.

A sample is used to obtain a 95% confidence interval for the mean of a population. The confidence interval goes from 78.21 to 87.64. If the same sample had been used to test the null hypothesis that the mean of the population differs from 90, the null hypothesis could be rejected at a level of significance of 0.05.

There is an inverse relationship between the probabilities of Type I and Type II errors; as one increases, the other decreases, and vice versa.

If we want to compute the probability of a Type II error, which of the following statements is false?

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

The ____________________ of a test is a measure of its performance.