Question 1 :

QUESTION 1 A real estate agent claims that the mean price of houses is different from 17.8 thousand dollars. To check this claim, the prices of a random sample of 18 newly sold houses were recorded (thousand dollars). 16.1 15.716.918.5122141 17.216.7151 153143118 13613.3 11418.3 22316.3 Is there sufcient evidence at the 5% signicance level to conclude that the population mean debt at graduation is different from $17.8 ? Estimate the population mean with 95% condence. Solve the Problem in the following steps and Select the letter from (a, I), c or (1} below that corresponds to the correct answer. 1. Write the null Ho and alternative hypotheses H1 a 3) 110:1: - 17.3 H1: 1: .- 17.8 b) H1: .1: - 17.3 Ho: Iu .- 17.3 e) Ho: p - 11.8 H1: p .- 17.3 2. Test normality for the Data (from the Megastat) b a) P-value = 0.080 b) P-value = 0.945 c) P-value =0.04 3. The decision of the test of normality is 7 a a) population Is approximately normal b) population Is not normal 4. Verify the assumptions you need to make the test. (write your solution explicitly} c a) 2- test : population normal + standard deviation of the population Is unknown h) t- test : population normal 1- standard deviation oi the population is known c) t- test : population normal + standard deviation of the population Is unknown 5. Find Test statistic t and P-value [from the Mega-Stat) b a) t = 2.57 Pdvalue = 0.020 b) t = -2.51 P-value = 0.020 c) t = 0.020 Pwalue = -2.57 6. Test the hypothesis is (a) using Pvalue 3) Since the p-value ls more than 0.05, we reject H0 and conclude that the population mean debt at graduation ls different from $17.8 b) Since the p-value ls less than 0.05, we fall to reject H0 and we don't have evidence to conclude that the population mean debt at graduation is different from $17.8 c) Since the p-value ls less than 0.05, we reject H0 and conclude that the population mean debt at graduation is different from $17.3 7. Find Critical value of the statistical test in part (a), with 5% significance level a) df = 17 Critical value = 1.740 b) df = 17 Critical value = 2.11 c) df = 17 Critical value = 2.898 8. Test the hypothesis is (a) using Test statistic t a) Since t7 c) HO: H=7 . H1: H >7 2. What are the required conditions you need to make the test. b a) z-test, n above 30, and the standard deviation of the population is unknown b) t-test, n above 30, and the standard deviation of the population is unknown c) z-test, n above 30 and the standard deviation of the population is known 3. Find Test statistic t and P-value (from the Mega-Stat) a a) t = 2.36; P-value = 0.011 b) t=2.36 ; P-value = 0.009 c) t = 2.36; P-value =0.989 4. Test the hypothesis is (a) using P-value a a) Since the p-value is less than 0.05, we reject HO, and we can conclude that the number of sticks of gum a person chews per day actually greater than 7 b) Since the p-value is more than 0.05, we reject HO, and we can conclude that the number of sticks of gum a person chews per day actually greater than 7 c) Since the p-value is less than 0.05, we fail to reject HO, and we can conclude that the number of sticks of gum a person chews per day actually greater than 7 d) Since the p-value is more than 0.05, we reject HO, and we don't have evidence to conclude that the number of sticks of gum a person chews per day actually greater than 7 5. Find Critical value of the statistical test in part (a), at a = 0.05 d a) df =50 Critical value = 1.676 b) df=51 Critical value = 1.675 c) df=51 Critical value = 1.677 d) df= 49 Critical value = 1.677 6. Test the hypothesis is (a) using Test statistic t a) Since the test statistic is less than the critical value, we reject HO, and we can conclude that the number of sticks of gum a person chews per day actually greater than 7 b) Since the test statistic is more than the critical value, we reject HO, and we can conclude that the number of sticks of gum a person chews per day actually greater than 7 c) Since the test statistic is more than the critical value we fail to reject HO, and we can conclude that the number of sticks of gum a person chews per day actually greater than 7 7. Write the decision in the statement of the test you did in (4) and (6) a) There is an agreement between the hypothesis test using the p-value and the critical value. b) There is a disagreement between the hypothesis test using the p-value and the critical value.QUESTION 3 In some states, the law requires drivers to turn-on their headlights when driving in the rain. A highway patrol officer believes that different from one-fifth (20%) of all drivers follow this rule. As a test, he randomly samples 400 cars driving in the rain and counts the number whose headlights are turned-on and found this number 72. Does the officer have enough evidence at the 10% significance level to support his belief? Solve the Problem in the following steps and Select the letter from (a, b, c or d) below that corresponds to the correct answer. 1. Write the null Ho and alternative hypotheses H1 b a) HO:p # 0.2 H1:p=0.2 b) HO: p= 0.2 H1: p #0.2 c) HO: p # 0.2 H1:p#0.2 2. Verify the required conditions (Assumptions) a) z-test : n*p >5 and n*p 5 and n*(1-Po ) >5 c) z-test : n*p >5 and n*(1-p) >5 d) z-test : n*po >5 and n*(1-Po ) >5 3. Find Test statistic Z and P-value (from the Mega-Stat) a a) test statistic = -1 P-value = 0.317 b) test statistic = -1 P-value = 0.159 c) test statistic = -1 P-value = 0.841 4. Test the hypothesis is (a) using P-value c a) since the p-value is less than 0.1, we reject HO and we can conclude that the officer has enough evidence to support his belief b) since the p-value is more than 0.1, we reject HO and we can conclude that the officer has enough evidence to support his belief c) since the p-value is more than 0.1, we fail to reject HO and we don't have evidence to conclude that the officer has enough evidence to support his belief d) since the p-value is more than 0.1, we fail to reject HO and we can conclude that the officer has enough evidence to support his belief 5. Find Critical value for the statistical test in part (a), at 90% c a) Critical value = 2.326 b) Critical value = 1.282 c) Critical value = 1.645 6. test the hypothesis is (a) using Test statistic a) since the test statistic is more than the critical value, we reject HO and we can conclude that the officer has enough evidence to support his belief b) since the test statistic is less than the critical value we fail to reject HO and we don't have evidence to conclude that the officer has enough evidence to support his belief ) since the test statistic is less than the critical value, we reject HO and we can conclude that the officer has enough evidence to support his belief 8. Write the decision in the statement of the test you did in (4) and (6) a) there is a disagreement between the hypothesis test with the p-value and the critical value. b) there is an agreement between the hypothesis test with the p-value and the critical value.QUESTION 4 Problem4 (Use the Formula sheet and the Tables to answer this question, You should not use Mega-Stat) A statistics practitioner is in the production process wants to make a test to determine whether there is enough evidence to infer that the population production mean is different from 190 at the 5% significance level. She selected a random sample of 200 process and found it has mean 182 and standard deviation 20 Solve the Problem in the following steps and Select the letter from (a, b, c or d) below that corresponds to the correct answer. 1. Write the null Ho and alternative hypotheses HI b a) HO: H = 190, H1: /=190 b) HO: H= 190, H1: H =190 C) HO: H= 182, H1: H = 182 2. Verify the required assumptions? c a) z- test : n>30+ standard deviation of the population is unknown b) t- test : n30+ standard deviation of the population is unknown 3. Calculate the value of the test t (Use formula sheet) a a) t test is -5.65685 o) z test is -5.65685 c) t test is 5.65685 4. Find Critical value for this statistical test, at the 5% significance level (using the table) b a) Critical value = 1.96 b) Critical value = 2 c) Critical value = 1.671 5. Test the hypothesis in (a) is using the test statistic method c a) Test statistic t= -5.657