Exam 9: Hypothesis Testing: Single Population

The probability of rejecting a true null hypothesis is denoted by β.

The Next Questions Are Based On The Following Information: Consider a problem with the hypothesis test H₀ : μ = 4 against H₁ : μ > 4,and the following decision rule: Reject H₀ if > 1.645 -Compute the probability of Type II error and the power of the test for μ = 4.0

Suppose that you want to test H₀ : P = 0.55 against H₁: P ≠ 0.55.The appropriate critical values are:

The Next Questions Are Based On The Following Information: The marketing department for a hand calculator claims the battery pack performs 20,000 calculations before it has to be recharged.The quality control manager for the manufacturer is entrusted with validating the claim that the battery pack works as long as the specifications state in order to secure a large order from a key customer.A test of 114 battery packs yields an average of 19,695 calculations with a standard deviation of 1,103. -Formulate the appropriate null and alternative hypotheses.

The Next Questions Are Based On The Following Information: An alcohol brewery firm claims that the proportion of alcohol in their new drink is at most 10 percent.A random sample of 100 bottles of the drink were selected and found to consist of 9 percent alcohol. -What is the p-value for this test?

The Next Questions Are Based On The Following Information: A team of builders has surveyed buyers of their new homes for years.Consistently,only 41% of the buyers have indicated that they were "quite satisfied" or "very satisfied" with the construction quality of their homes.The builders have implemented new procedures and adopted a revised quality-inspection system to ultimately improve customer satisfaction.They have surveyed 104 buyers since implementing changes;these buyers seem representative,with no systematic changes from past purchasers.Of the 104 buyers,52 indicated they were quite or very satisfied. -Test the null hypothesis with the alternative hypothesis,H₁ : P > 0.41,at α = 0.05

A gaming control board claims that the average household income of those people playing blackjack at casinos is at least $50,000.Assume that the distribution of household income of those people playing blackjack is normally distributed with a standard deviation of $7,559.Suppose that for a sample of 45 households,it is found that the average income was $48,326.Is the gaming control board incorrect in asserting that the average household income of blackjack players is at least $50,000? Use the 10 per cent significance level.

If a researcher fails to reject the null hypothesis,then the alternative hypothesis should be accepted.

The Next Questions Are Based On The Following Information: An alcohol brewery firm claims that the proportion of alcohol in their new drink is at most 10 percent.A random sample of 100 bottles of the drink were selected and found to consist of 9 percent alcohol. -What conclusions can be drawn using a level of significance equal to 0.10?

Match the symbol β with the correct definition.

Explain carefully the distinction between simple and composite hypotheses.

A magazine advertises that at least 65% of all their readers are women.A woman's group wants to test this assertion and they take a sample of 300 households,and find that only 61.3% of the readers are women.From the data,is there sufficient evidence to doubt the magazine's claim at a 10% level of significance?

The manufacturer of bags of cement claims that they fill each bag with at least 50.2 pounds of cement.Assume that the standard deviation for the amount in each bag is 1.2 pounds.The decision rule is adopted to shut down the filling machine if the sample mean weight for a sample of 40 bags is below 49.8.Suppose that the true mean weight of bags is 50 pounds.Using this decision rule,what is the probability of a Type II error?

The Next Questions Are Based On The Following Information: The marketing department for a hand calculator claims the battery pack performs 20,000 calculations before it has to be recharged.The quality control manager for the manufacturer is entrusted with validating the claim that the battery pack works as long as the specifications state in order to secure a large order from a key customer.A test of 114 battery packs yields an average of 19,695 calculations with a standard deviation of 1,103. -Calculate the appropriate test statistic and p-value.

The Next Questions Are Based On The Following Information: Before agreeing to purchase a large order of polyethylene sheaths for a particular type of high pressure oil-filled submarine power cable,a company wants to see conclusive evidence that the true standard deviation of sheath thickness is less than .05 inches. -In this test,what would be a Type II error?

The Next Questions Are Based On The Following Information: In a random sample of 200 high school students,92 sample members indicated some measure of agreement with this statement:"A prospective university's academic ranking and image is important to my decision to attend that institution." -The Discovery Automobile Company is attempting to determine if it should retain a previously popular sports car model called El Nino.A random sample of 500 consumers is obtained,and each person in the sample is asked if he/she would still consider purchasing an El Nino.To determine if El Nino should be retained,the sample proportion of respondents who said yes, ,is used at a level α = 0.05 to test the hypothesis H₀ : P ≥ 0.5 against H₁ : P < 0.5.What value of the sample proportion, ,is required to reject the null hypothesis?

Increasing the probability of a Type I error by one percent decreases the probability of a Type II error by one percent.

The Next Questions Are Based On The Following Information: An insurance company employs agents on a commission basis.It claims that in their first year,agents will earn a mean commission of at least $42,000 and that the population standard deviation is no more than $6,800.A random sample of nine agents found,for commissions in the first year, and The population distribution can be assumed to be normal. -What are the appropriate null and alternative hypotheses?

The Next Questions Are Based On The Following Information: The U.S.Postal Service advertises that at least 63.4% of all third class mail is read by the recipients.An environmental group,concerned about waste production wants to test this assertion.They take a sample of 220 households and find that only 58.7% read their third class mail. -What are the null and alternative hypotheses for the environmental group's test?

The Next Questions Are Based On The Following Information: An accountant claims to be able to complete a standard tax return in under an hour.For a random sample of 24 tax returns,the accountant averaged 63.2 minutes with a standard deviation of 7.7 minutes. -What is the most accurate estimate of the p-value?