Exam 10: Hypothesis Testing

A(n) ________ hypothesis is the statement that is being tested. It usually represents the status quo, and it is not rejected unless there is convincing sample evidence that it is false.

Assuming a fixed sample size, as α (Type I error) decreases, β (Type II error) ________.

A recent study conducted by the state government attempts to determine whether the voting public supports a further increase in cigarette taxes. The opinion poll recently sampled 1,500 voting age citizens. 1,020 of the sampled citizens were in favor of an increase in cigarette taxes. The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66. Using the critical value rule, at α = .10, we would not reject H₀.

Using the critical value rule, if a two-sided null hypothesis is rejected for a single mean at a given significance level, 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 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 appropriate test statistic to test the claim that at least 50 percent of journalism majors agree with the statement.

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. Using the critical value rule, at α = .05, we do not reject H₀.

The manufacturer of an over-the-counter heartburn relief medication claims that its product brings relief in less than 3.5 minutes, on average. To be able to make this claim, the manufacturer was required by the FDA to present statistical evidence in support of the claim. The manufacturer reported that for a sample of 50 heartburn sufferers, the mean time until relief was 3.3 minutes and the population standard deviation was 1.1 minutes. Calculate the p-value that corresponds to the test statistic that would be used in applying the p-value rule.

Using the p-value rule, if a null hypothesis is rejected at a significance level of .05, it will ________ be rejected at a significance level of .01.

To apply the p-value rule, determine the p-value for H₀: p = .5; versus H_A: p ≠.5, when n = 225 and = .54 (α = .05).

In testing H₀: p ≥ .33; versus H_A: p < .33 using the critical value rule, with = .20 and n = 100, what is the value of the test statistic?

Determine the p-value for H₀: p ≤ .5; versus H_A: p > .5, when n = 225 and = .54 (α = 0.05).

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. What is the critical value used to test the claim at α = .05?

A random sample of 80 companies who announced corrections to their balance sheets took a mean time of 8.1 days for the time between balance sheet construction and the complete audit. The population standard deviation is assumed to be 1.3 days. What is the critical value for α = .001 to apply the critical value rule for the claim that μ is greater than 7.5 days?

In an early study, researchers at Ivy University found that 33 percent of the freshmen had received at least one A in their first semester. Administrators are concerned that grade inflation has caused this percentage to increase. In a more recent study, of a random sample of 500 freshmen, 185 had at least one A in their first semester. Calculate the appropriate test statistic to test the hypotheses.

We are testing H₀: μ ≤ .95; versus H_A: μ > .95. When = .99, s = .12, and n = 24, at alpha = .05, we reject H₀. Assume that the population from which the sample is selected is normally distributed.

Consider an engine parts supplier and suppose the supplier has determined that the mean and variance of the population of all cylindrical engine part outside diameters produced by the current machine are, respectively, 2.5 inches and .00075. To reduce this variance, a new machine is designed. A random sample of 20 outside diameters produced by this new machine has a sample mean of 2.5 inches and a variance of s² = .0002 (normal distribution). In order for a cylindrical engine part to give an engine long life, the outside diameter must be between 2.43 and 2.57 inches. If σ² denotes the variance of the population of all outside diameters that would be produced by the new machine, test H₀: σ² = .00075 versus H_a: σ² < .00075 by setting α = .05.

The value of the test statistic is compared with a(n) ________ in order to decide whether the null hypothesis can be rejected.

The power of a statistical test is the probability of rejecting the null hypothesis when it is false.

It is estimated that the average person in the United States uses 123 gallons of water per day. Some environmentalists believe this figure is too high and conduct a survey of 40 randomly selected Americans. They find a mean of 113.03 gallons and a population standard deviation of 25.99 gallons. Calculate the p-value for this test statistic and test the hypothesis at α = .01 using the p-value rule.

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. What is the p-value that would be used in applying the p-value rule?