Exam 10: Hypothesis Testing

A survey of the wine market has shown that the preferred wine for 17 percent of Americans is merlot. A wine producer in California, where merlot is produced, believes the figure is higher in California. She contacts a random sample of 550 California residents and asks which wine they purchase most often. Suppose 115 reply that merlot is the primary wine. Using the p-value rule, calculate the p-value associated with the test statistic, and test the claim at α = .01.

The manager of a local specialty store is concerned with a possible slowdown in payments by her customers. She measures the rate of payment in terms of the average number of days receivables are outstanding. Generally, the store has maintained an average of 50 days. A random sample of 25 accounts gives an average of 54 days outstanding with a standard deviation of 8 days. Calculate the appropriate test statistic to apply the critical value rule.

When the null hypothesis is true, there is no possibility of making a Type I error.

Last year, TV station KAAA had a share of the 6 p.m. news audience approximately equal to, but not greater than, 25 percent. The advertising department for the station believes the current audience share is higher than the 25 percent share they had last year. In an attempt to substantiate this belief, the station surveyed a random sample of 400 viewers of 6 p.m. news and found that 146 watched KAAA. Test these hypotheses at α = .001 using the critical value rule.

For the following hypothesis test, where H₀: μ ≤ 10; vs. H_A: μ > 10, we reject H₀ at level of significance α and conclude that the true mean is greater than 10, when the true mean is really 8. Based on this information, we can state that we have

Using the p-value rule for a population proportion or mean, if the level of significance is less than the p-value, the null hypothesis is rejected.

A microwave manufacturing company has just switched to a new automated production system. Unfortunately, the new machinery has been frequently failing and requiring repairs and service. Historically, the company has been able to provide its customers with a completion time of 6 days or less. To analyze whether the completion time has increased, the production manager took a sample of 36 jobs and found that the sample mean completion time was 6.5 days with a sample standard deviation of 1.5 days. At a significance level of .10 using the critical value rule, we can show that the completion time has increased.

We are testing H₀: μ ≥ 22; versus H_A: μ < 22. Given α = .01, n = 100, = 21.431, and σ = 1.295, we should not reject H₀.

If you live in California, the decision to buy earthquake insurance is an important one. A survey revealed that only 133 of 337 randomly selected residences in one California county were protected by earthquake insurance. What is the p-value associated with the test statistic calculated to test the claim that less than 40 percent of the county residents are protected by earthquake insurance?

Using the critical value rule, if a two-sided null hypothesis cannot be rejected for a single mean at a given significance level, then the corresponding one-sided null hypothesis (i.e., the same sample size, the same standard deviation, and the same mean) will ________ be rejected at the same significance level.

A survey of the wine market has shown that the preferred wine for 17 percent of Americans is merlot. A wine producer in California, where merlot is produced, believes the figure is higher in California. She contacts a random sample of 550 California residents and asks which wine they purchase most often. Suppose 115 reply that merlot is the primary wine. Calculate the appropriate test statistic to test the hypotheses.

In order to make statistical inferences about σ² that are valid using a chi-square distribution, the assumption is that the sampled population is also a chi-square distribution.

The ________ hypothesis will be accepted only if there is convincing sample evidence that it is true.

Assuming that the null hypothesis is true, the ________ is the probability of observing a value of the test statistic that is at least as extreme as the value actually computed from the sample data.

A sample of 400 journalism majors at a major research university was asked if they agreed with the following statement: "Government should be more involved in the oversight and regulation of reporting." Fifty-two percent of the respondents agreed with the statement. Calculate the p-value associated with the test statistic and test at α = .05 using the p-value rule testing the hypothesis if more than 50% of journalists agreed with this sentiment.

We test H₀: μ ≤ 3.0; versus H_A: μ > 3.0. If = 3.44, s = .57, and n = 13, at a significance level of .05, we do not reject H₀. Assume that the population from which the sample is selected is normally distributed.

In 1930, the average size of a public restroom was 172 square feet. By 1990, due to federal disability laws, the average size had increased to 471 square feet. Suppose that a design team believes that this standard has increased from the 1990 level. They randomly sample 23 public restrooms in a major midwestern city and obtain a mean square footage of 498.78 with a standard deviation of 46.94. Calculate the appropriate test statistic to test the hypotheses.

We are testing H₀: μ ≤ 8; versus H_A: μ > 8. Given α = .01, n = 25, = 8.112, and s = .16, we should reject the H₀. Assume that the population from which the sample is selected is normally distributed.

Based on a random sample of 25 units of product X, the average weight is 102 lb and the sample standard deviation is 10 lb. We would like to decide if there is enough evidence to establish that the average weight for the population of product X is greater than 100 lb. Assume the population is normally distributed. Therefore, the alternative hypothesis can be written as H_A: μ > 100.

When evaluating a new process, using the square root of the upper end of the confidence interval for σ² gives an estimate of the smallest that σ for the new process might reasonably be.