Exam 10: Hypothesis Testing

A manufacturer of salad dressings uses machines to dispense liquid ingredients into bottles that move along a filling line. The machine that dispenses dressing is working properly when 8 ounces are dispensed. The standard deviation of the process is .15 ounces. A sample of 48 bottles is selected periodically and the filling line is stopped if there is evidence that the mean amount dispensed is different from 8 ounces. Suppose that the mean amount dispensed in a particular sample of 48 bottles is 7.983 ounces. Calculate the test statistic.

The level of significance, α, indicates the probability of rejecting a false null hypothesis.

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 14. Based on this information, we can state that we have

The manager of a grocery store wants to determine whether the amount of water contained in 1-gallon bottles purchased from a nationally known manufacturer actually averages 1 gallon. It is known from the specifications that the standard deviation of the amount of water is equal to .02 gallon. A random sample of 32 bottles is selected, and the mean amount of water per 1-gallon bottle is found to be .995 gallon. Calculate the p-value and test whether the specifications are being met at α = .001 using the p-value rule.

It can be established at α = .05 that a majority of students favor the plus/minus grading system at a university if in a random sample of 500 students, 270 favor the system.

The local pharmacy prides itself on the accuracy of the number of tablets that are dispensed in a 60-count prescription. The new manager feels that the pharmacy assistants might have become careless in counting due to an increase in the volume of prescriptions. To test her theory, she randomly selects 40 prescriptions requiring 60 tablets and recounts the number in each bottle. She finds a sample mean of 62.05 and a standard deviation of 4.45. Calculate a confidence interval to test the hypotheses at α = .002 and interpret the result.

A test statistic is computed from sample data in hypothesis testing and is used in making a decision about whether or not to reject the null hypothesis.

The manager of the quality department for a tire manufacturing company wants to know the average tensile strength of rubber used in making a certain brand of radial tire. The population is normally distributed and the population standard deviation is known. She uses a z test to test the null hypothesis that the mean tensile strength is less than or equal to 800 pounds per square inch. The calculated z test statistic is a positive value that leads to a p-value of .067 for the test. If the significance level for this test is .10, the null hypothesis would be rejected.

When testing a hypothesis about a single mean, a sample size of 200 is selected from a normally distributed population. If the population standard deviation is known, the correct test statistic to use is ________.

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. Identify the null hypothesis.

In a sample of n = 16 selected from a normally distributed population, we find a population standard deviation of s = 10. What is the value of χ² if we are testing H₀: σ² = 144?

In testing H₀: μ ≤ 23; versus H_A: μ > 23 using the critical value rule, when = 26, σ = 6, and n = 30, what is the value of the test statistic?

Alpha (α) is the probability that the test statistic would assume a value at or more extreme than the observed value of the test.

According to a national survey, the average commuting time for people living in a city with a population of 1 to 3 million is 19.0 minutes. Suppose a researcher lives in a city with a population of 2.4 million and wants to test this claim for her city. Taking a random sample of 20 commuters, she calculates a mean time of 19.346 minutes and a standard deviation of 2.842 minutes. Calculate the appropriate test statistic to test the hypotheses.

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 p-value associated with the test statistic and test the claim at α = .05 using the p-value rule.

________ is not rejecting H₀ when H₀ is false.

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 whether 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 = .01, we can reject the null hypothesis.

For a given hypothesis test, if we do not reject H₀, and H₀ is true,

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

When testing a hypothesis about a single mean, if the sample size is 20, the population standard deviation is unknown, and the population is assumed to be a normal distribution, the correct test statistic to use is ________.