Question

Complete: Chapter 8 Problem Set Back to Assignment Attempts Average: 4/8 12. Computing power As Aa Suppose an architectural firm specializing in the structural restoration and renovation of historic homes and early barns is deciding whether to open a branch of the company in Wilmington, Vermont. Market research commissioned by the firm indicates that the Vermont location will be profitable only if the mean age of houses and bans located within a 100-mile radius of wilmington is greater than 65 years The architectural firm conducts a hypothesis test to determine whether u, the mean age of structures located within a 100-mile radius of wilmington, is greater than 65 years. The test is conducted a05 level of significance using a random sample of n- 64 houses and barms located in the specified area. The population standard deviation of the age of structures is assumed to be known with a value of a-11.2 years. The firm will open a Vermont branch only if it rejects the null hypothesis that the mean age of structures in the specified area is less than or equal to 65 years. To summarize this hypothesis test refer to the chart given below. Reject the Null-Open the Branch Fail to Reject Do Not Open the Branch If, on the basis of the hypothesis test, the architectural firm decides to open a branch, but the true mean age of houses and bams located within a 100-mie radius of wilmington is less than 65 years, the firm has committed a error, because this branch will be unprofitable If, on the basis of the hypothesis test, the architectural firm decides not to open a branch, but the true mean age of houses and bams located within a 100-mie radius of wilmington is greater than 65 years, the firm has committed a eror, because this branch would have been profitable Use the Distributions tool to help you answer the questions that folfow. shanan D o3 CENGAGE MINDTAP Complete: Chapter 8 Problem Set Use the Distributions tool to help you answer the questions that follow. Normal Distribubion Mean 68.0 Standard Devistion 3.0 69 60 65 66 61 621 AA The null hypothesis is rejected when the sample mean M is architectural firm will make the decision not to open a branch in Vermont if M is (Hint: To use the tool, set the Mean to the hypothesized mean (65) and the Standard Deviation to the standard deviation of the sampling distribution of M.) Therefore, the Suppose that the true value of u is 67 years. The probability that the architecture firm commits a Tpe II error is (Hint: To use the tool, set the Mean to the true mean (67) and position the vertical line at the critical value of M 67.30.) If the true value of u is 67 years, the power of the test is Based on the level of significance it has selected for its test, the architectural firm is willing to risk a probability of opening an unprofitable branch. It is willing to risk a 0.20 probability of not opening the branch when M67 (In other words, it is willing to fail to reject the null hypothesis when it actually should have rejected the null hypothesis only 20 % of the time.) What should the firm do? O Decrease its sample size. O Decrease a O Increase its sample size. O do nothing: its current isks ere acceptable N

Answer 1

Answer: ---- Date: ----18/6/2019

Type I

Type II

The claim is that the mean age of houses and barns located within a 100-mle radius of Wilmington is greater than 65 years The null and alternative hypotheses are, Null hypothesis Ho us 65 Alternative hypothesis Hi 65 n 64, 68 (from graph),o 11.2 and a 0.05 tailed, the critical value at a 0.05 from the normal tables is 1.645 From the given information, = Since the test is one The null hypothesis is rejected if the sample mean is greater than, 11.2 65 1.645 V64 65 2.303 67.303 67.30 mean M is greater than or equal to 67.30 The null hypothesis is rejected when the sample therefore, the architectural firm will make the decision not to open a branch in Vermont if M is less than 67.30. suppose that the value of uis 67 years. The probability that the architecture firm commits a Туре II error is,

P(Type II error) P(Accept H H, is true) P(M 67.30 | 4 67) M- 67.30 67 11.2 σ n 64 P(Zs 0.21) (using excel function (NORMSDIST(0.21)) |0.5832 If the true value of uis 67 years, the power of the test is, Power 1-P(Type II error) -1-0.5832 0.4168 Based on the level of significance it has selected for its test, the architectural firm is willing to risk a 0.5832 probability of opening an unprofitable branch. It is willing to risk a 0.20 probability of not opening the branch when 67. So, the firm should increase its sample size.