Exam 9: Introduction to Hypothesis Testing

A consumer group plans to test whether a new passenger car that is advertised to have a mean highway miles per gallon of at least 33 actually meets this level.They plan to test the hypothesis using a significance level of 0.05 and a sample size of n = 100 cars.It is believed that the population standard deviation is 3 mpg.Based upon this information,if the "true" population mean is 32.0 mpg,what is the probability that the test will lead the consumer group to "accept" the claimed mileage for this car?

The U.S.Bureau of Labor Statistics (www.bls.gov)released its Consumer Expenditures report in October 2008.Among its findings is that average annual household spending on food at home was $3,624.Suppose a random sample of 137 households in Detroit was taken to determine whether the average annual expenditure on food at home was less for consumer units in Detroit than in the nation as a whole.The sample results are in the file Detroit Eats.Based on the sample results,can it be concluded at the α = 0.02 level of significance that average consumer-unit spending for food at home in Detroit is less than the national average?

Given the following null and alternative Test the hypothesis using α = 0.01 assuming that a sample of n = 200 yielded x = 105 items with the desired attribute.

For the following z-test statistic,compute the p-value assuming that the hypothesis test is a one-tailed test: z = -1.55.

For the following z-test statistic,compute the p-value assuming that the hypothesis test is a one-tailed test: z = 1.34.

A mail-order business prides itself in its ability to fill customers' orders in six calendar days or less on the average.Periodically,the operations manager selects a random sample of customer orders and determines the number of days required to fill the orders.Based on this sample information,he decides if the desired standard is not being met.He will assume that the average number of days to fill customers' orders is six or less unless the data suggest strongly otherwise.On one occasion where a sample of 40 customers was selected,the average number of days was 6.65,with a sample standard deviation of 1.5 days.Can the operations manager conclude that his mail-order business is achieving its goal? Use a significance level of 0.025 to answer this question.

You are given the following null and alternative hypotheses: If the true population mean is 4,345,determine the value of beta.Assume the population standard deviation is known to be 200 and the sample size is 100.

If the hypothesis test you are conducting is a two-tailed test,which of the following is a possible step that you could take to increase the power of the test?

A hypothesis test is to be conducted using an alpha = .05 level.This means:

According to data from the Environmental Protection Agency,the average daily water consumption for a household of four people in the United States is approximately at least 243 gallons.(Source: http://www.catskillcenter.org/programs/csp/H20/Lesson3/house3.htm)Suppose a state agency plans to test this claim using an alpha level equal to 0.05 and a random sample of 100 households with four people. State the appropriate null and alternative hypotheses.

You are given the following null and alternative hypotheses: If the true population mean is 1.25,calculate the power of the test.Assume the population standard deviation is known to be 0.50 and the sample size is 60.

A mail-order business prides itself in its ability to fill customers' orders in six calendar days or less on the average.Periodically,the operations manager selects a random sample of customer orders and determines the number of days required to fill the orders.Based on this sample information,he decides if the desired standard is not being met.He will assume that the average number of days to fill customers' orders is six or less unless the data suggest strongly otherwise.Establish the appropriate null and alternative hypotheses.

A conclusion to "not reject" the null hypothesis is the same as the decision to "accept the null hypothesis".

A major issue facing many states is whether to legalize casino gambling.Suppose the governor of one state believes that more than 55% of the state's registered voters would favor some form of legal casino gambling.However,before backing a proposal to allow such gambling,the governor has instructed his aides to conduct a statistical test on the issue.To do this,the aides have hired a consulting firm to survey a simple random sample of 300 voters in the state.Of these 300 voters,175 actually favored legalized gambling. State the appropriate null and alternative hypotheses.

A company makes a device that can be fitted to automobile engines to improve the mileage.The company claims that if the device is installed,owners will observe a mean increase of more than 3.0 mpg.Assuming that the population standard deviation of increase is known to be 0.75 mpg,and a sample of size 64 cars is selected with an = 3.25 mpg,use the p-value approach to test the null hypothesis using a significance level of 0.05.

The chance of making a Type II statistical error increases if the "true" population mean is closer to the hypothesized population mean,all other factors held constant.

A company that makes shampoo wants to test whether the average amount of shampoo per bottle is 16 ounces.The standard deviation is known to be 0.20 ounces.Assuming that the hypothesis test is to be performed using 0.10 level of significance and a random sample of n = 64 bottles,which of the following would be the upper tail critical value?

When someone is on trial for suspicion of committing a crime,the hypotheses are: H₀ : innocent H_A : guilty Which of the following is correct?

You are given the following null and alternative hypotheses: If the true population mean is 1.25,determine the value of beta.Assume the population standard deviation is known to be 0.50 and the sample size is 60.

For the following hypothesis test: With n = 15,s = 7.5,and = 62.2,state the conclusion.