Exam 9: Hypothesis Testing: Single Population

The Next Questions Are Based On The Following Information: The state lottery office claims that the average household income of those people playing the lottery is at least $37,000.Assume that the distribution of household income of those people playing the lottery is normally distributed with a standard deviation of $5,756.Suppose that for a sample of 25 households,it is found that the average income was $36,243. -What is the test statistic for this test?

The Next Questions Are Based On The Following Information: Suppose that you want to test H₀ = μ = 0.54 against H₁ :μ < 0.54 based on a sample of n = 25 and s = 13.2. -What is the test statistic?

The Next Questions Are Based On The Following Information: An engineering research center claims that,through the use of a new computer control system,automobiles should achieve,on average,at least an additional 5 miles per gallon of gas.A random sample of 81 automobiles was used to evaluate this product.The sample mean increase in miles per gallon achieved was 4.5,and the sample standard deviation was 2.9 miles per gallon. -When is the chi-square distribution test not reliable for testing in hypothesis tests?

Increasing the significance level of a test increases the probability of a Type II error.

The Next Questions Are Based On The Following Information: A beer producer claims that the proportion of its customers who cannot distinguish regular from light beer is at most 12 percent.The producer decides to test this null hypothesis against the alternative that the true proportion is more than 12 percent.The decision rule adopted is to reject the null hypothesis if the sample proportion of who cannot distinguish between the two beers exceeds 15 percent. -Suppose that the true proportion of customers who cannot distinguish between these flavors is 0.10.If a random sample of 100 customers is selected,what is the probability of a Type II error?

Match the symbol (1- α)with the correct definition.

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 -Rewrite the decision rule explicitly in terms of .

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. -What kind of alternative hypothesis type would fit such a survey?

The Next Questions Are Based On The Following Information: A pharmaceutical manufacturer is concerned that the mean impurity concentration in pills should not exceed 3%.It is known that from a particular production run impurity concentrations follow a normal distribution with a standard deviation 0.4%.A random sample of 36 pills from a production run was checked,and the sample mean impurity concentration was found to be 3.09%. -In the context of this problem,explain why a one-sided alternative hypothesis is more appropriate than a two-sided alternative.

The Next Questions Are Based On The Following Information: The manufacturer of a new chewing gum claims that at least 80% of dentists surveyed prefer their type of gum and recommend it for their patients who chew gum.An independent consumer research firm decides to test their claim.The findings in a sample of 200 dentists indicate that 74.1% of the respondents do actually prefer their gum. -What are the null and alternative hypotheses for the test?

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. -Which of the following statements is most accurate?

The Next Questions Are Based On The Following Information: Research and development has designed a ball point pen so that the true average writing lifetime under controlled conditions (involving the use of a writing machine)is at least 12 hours.A random sample of 18 pens is selected,the writing lifetime of each is determined,and a normal probability plot of the resulting data supports the use of a one-sample t test. -What conclusion is appropriate for the hypotheses H₀ : μ = 12 against H₁ : μ < 12,and the test statistic t = -2,and α = .01?

Explain the distinction between the significance level and the power of the test.

The Next Questions Are Based On The Following Information: An engineering research center claims that,through the use of a new computer control system,automobiles should achieve,on average,at least an additional 5 miles per gallon of gas.A random sample of 81 automobiles was used to evaluate this product.The sample mean increase in miles per gallon achieved was 4.5,and the sample standard deviation was 2.9 miles per gallon. -Find the p-value of this test,and interpret the results.

Suppose that a t test of H₀ : μ = 250 against H₁ : μ > 250 is based on 10 degrees of freedom.If the calculated value of the test statistic is t = 2.228,then the p-value for this test is 0.025.

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." -Find and interpret the p-value of the test.

The Next Questions Are Based On The Following Information: A hydraulic press is operating correctly when the standard deviation of the pressure is less than 120 pounds-per-square-inch (psi).Suppose you take a random sample of 15 measurements throughout the day of the psi and find the standard deviation to be 148.Suppose you want to test whether the press is operating correctly. -What is the decision rule for this test?

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= 4.04.

The larger the sample size,the greater the power of the test with everything else being equal.

The Next Questions Are Based On The Following Information: A company selling new econometrics computer software advertises that firms using this software obtain,on average during the first year,a yield of at least 10% on their initial investments.A random sample of 10 of the franchises that used the software produced the following yields for the first year of operation: 9.4,11.1,10.4,10.5,11.2,8.2,8.5,4.0,8.8,and 6.1.Assume that population yields are normally distributed. -On the basis of a random sample the null hypothesis: H₀ : μ ≤ μ₀ is tested against the alternative: H₁ : μ > μ₀ and the null hypothesis is not rejected at the 10% significance level.Does this necessarily imply that μ₀ is contained in the 90% confidence interval for μ?