Exam 9: Hypothesis Testing: Single Population

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. -For a two-tailed test at the 0.05 significance level,what is the rejection region when n is large and the population standard deviation is known?

Give an account of how a decision is made concerning the null hypothesis.

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. -A random sample of size 10 is selected from a normal population,where the population standard deviation is unknown.Assume that a two-tailed test at the 0.10 significance level is to be used.For what value of t will the null hypothesis not be rejected?

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. -Rosanne is the floor manager at Yesbe Beauty Products,who takes care of the face cream section.One of her tasks is to make sure that the face cream mini packs weigh four ounces (4.0)on average.Assume that the standard deviation of the weight of the mini packs is known to be 0.1 ounces.Rosanne tasks one of her employees to choose 25 packs at random and find the average weight.For what values would Rosanne tell the employee to reject the production,if she wanted the probability of a Type I error to be 0.10 or less?

The Next Questions Are Based On The Following Information: The dean of a business college in the Midwest claims that he can correctly identify whether a student is a finance major or a music industry management major by the way the student dresses.Suppose in actuality that he can correctly identify finance majors 84% of the time,while 16% of the time he mistakenly identifies a music industry management major as a finance major.Presented with one student and asked to identify the major of this student (who is either a finance or music industry management major),the dean considers this to be a hypothesis test with the null hypothesis being that the student is a finance major and the alternative that the student is a music industry management major. -Which of the following statements is an example of power of the 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 appropriate critical value?

Suppose that a test procedure about the population proportion P is performed,and that the sample proportion is approximately normally distributed.If the alternative hypothesis is H₁ : P ≠ P₀,then the rejection region for a level α = 0.05 is either Z < -1.96 or Z > 1.96.

Suppose a test procedure about the population mean μ is performed,when the population is normal with an unknown variance.If a sample of size 16 is drawn from the population and the alternative hypothesis is H₁ : μ ≠ μ₀,the null hypothesis is rejected at a level α = 0.05 if either t < -2.131 or t > 2.131.

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. -The value of the test statistic is:

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. -How is the probability β making a Type II error found in population proportion tests?

The Next Questions Are Based On The Following Information: A small community college claims that their average class size is equal to 35 students.This claim is being tested with a level of significance equal to 0.02 using the following sample of class sizes: 42,28,36,47,35,41,33,30,39,and 48.Assume class sizes are normally distributed. -Suppose you have the following null and alternative hypotheses: H₀ : μ = 8.3 and H₁ : μ ≠ 8.3.You take a sample of 30 observations,and find a sample mean of 7.3 with a standard deviation of 3.2.Which of the following is the most accurate statement about the p-value?

The Next Questions Are Based On The Following Information: A small community college claims that their average class size is equal to 35 students.This claim is being tested with a level of significance equal to 0.02 using the following sample of class sizes: 42,28,36,47,35,41,33,30,39,and 48.Assume class sizes are normally distributed. -Which distribution is most appropriate to perform this hypothesis test?

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. -A company produces electrical devices operated by a thermostatic control.According to the engineering specifications,the standard deviation of the temperature at which these controls actually operate should not exceed 2.0 degrees Fahrenheit.For a random sample of 25 of these controls,the sample standard deviation of operating temperatures was 2.36 degrees Fahrenheit.Stating any assumptions you need to make,test at the 5% level the null hypothesis that the population standard deviation is at most 2.0 against the alternative that is bigger.

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. -State the appropriate null and alternative hypotheses.

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 are the appropriate null and alternative hypotheses?

How is hypothesis testing a counterfactual argument?

The Next Questions Are Based On The Following Information: The dean of a business college in the Midwest claims that he can correctly identify whether a student is a finance major or a music industry management major by the way the student dresses.Suppose in actuality that he can correctly identify finance majors 84% of the time,while 16% of the time he mistakenly identifies a music industry management major as a finance major.Presented with one student and asked to identify the major of this student (who is either a finance or music industry management major),the dean considers this to be a hypothesis test with the null hypothesis being that the student is a finance major and the alternative that the student is a music industry management major. -The manufacturer of bags of cement claims that they fill each bag with at least 50.1 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 49.7.What is the probability of a Type I error?

The Next Questions Are Based On The Following Information: The supervisor of a production line believes that the average time to assemble an electronic component is 14 minutes.Assume that assembly time is normally distributed with a standard deviation of 3.4 minutes.The supervisor times the assembly of 14 components,and finds that the average time for completion is 11.6 minutes. -What is the z-value for a two-sided test of hypothesis for a population mean when the probability of rejecting a true null hypothesis is equal to .05?

The Next Questions Are Based On The Following Information: Manufacturing planning wants to estimate plant capacity in order to schedule customer orders and improve on-time delivery.A random sample of ten days output gave the following results for numbers of finished components produced: 577,642,615,655,600,570,640,620,595,and 575.Planning is concerned about the variability of daily output and views as undesirable any variance above 525. -A large milling machine produces steel rods.The machine is considered to be operating within customer specifications if the standard deviation of the diameter of the rods is 0.15 inches.As line supervisor,you need to demonstrate whether the machine is capable of meeting customer specifications.Based on a sample of 25 rods,the sample standard deviation is 0.19.Is there sufficient evidence at the 5% significance level to conclude that the machine is not operating within the customer tolerances?

The Next Questions Are Based On The Following Information: Manufacturing planning wants to estimate plant capacity in order to schedule customer orders and improve on-time delivery.A random sample of ten days output gave the following results for numbers of finished components produced: 577,642,615,655,600,570,640,620,595,and 575.Planning is concerned about the variability of daily output and views as undesirable any variance above 525. -Calculate the sample variance.