Exam 9: Hypothesis Testing

The rejection of a true null hypothesis is called a ______________ error.

Based on a random sample of 25 units of product X,the average weight is 102 lbs.and the sample standard deviation is 10 lbs.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 lbs.Assume the population is normally distributed.What is the critical value to test the claim at α = .01?

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 1500 voting age citizens.1020 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.What is the critical value to test the claim at α = .10?

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 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.

We are testing H₀: ? ? 22;versus H_A: ? < 22.Given ? = .01,n = 100, $\bar { X } = 21.431$ and ? = 1.295,we should not reject H₀.

If a null hypothesis is rejected at a significance level of .01,it will ____________ be rejected at a significance level of .05

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.

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 replied that merlot was the primary wine.Calculate the appropriate test statistic to test the hypotheses.

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

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.

One survey conducted by a major leasing company determined that the Lexus is the favorite luxury car for 25 percent of leases in Atlanta.Suppose a US car manufacturer conducts its own survey in an effort to determine whether this figure is correct.Of the 384 leases in Atlanta surveyed,79 lease a Lexus.Calculate the appropriate test statistic to test the hypotheses.

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.

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

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

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 0.15 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.

As the level of significance α increases,we are more likely to reject the null hypothesis.

According to a national survey,the average commuting time for people who commute to 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 in 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.

Based on a random sample of 25 units of product X,the average weight is 102 lbs.and the sample standard deviation is 10 lbs.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 lbs.Assume the population is normally distributed.What is the p-value for this test?

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

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