1 (Use MegaStat to answer this question) After the solution copy and pase the MegaStat output. 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 15.7 16.9 18.5 12.2 14.7 17.2 16.7 15.1 15.6 14.3 17.8 13.6 13.3 19.4 18.3 22.3 16.3 Is there sufficient evidence at the 5% significance level to conclude that the population mean debt at graduation is different from $17.8 ? Estimate the population mean with 95% confidence. Solve Problem1 in the following steps a. Write the null Ho and alternative hypotheses H1 b) Test normality for the Data (from the Mega-Stat) Ho: H1: P-value = Decision and Conclusion c) Verify the assumptions you need to make the test. (write your solution explicitly) d) Find Test statistic t and P-value (from the Mega-Stat) t = P-value = e) Test the hypothesis is (a) using P-value(write your solution explicitly) f) Find Critical value of the statistical test in part (a), with 5% significance level df = Critical value = g) Test the hypothesis is (a) using Test statistic t (write your solution explicitly) h) Estimate the population mean with 95% confidence (from the Mega-Stat output) U.L. = L.L. = i. Test the hypothesis is (a) using confidence interval method (write your solution explicitly) j) Write the decision in statement of the test you did in (e) and (g) and (i) (write your solution explicitly) Copy and paste the MegaStat output for problem 1 Problem2 (Use MegaStat to answer this question) After the solution copy and paste the MegaStat output. Recent study stated that on the average the number of sticks of gum he or she chewed daily more than 7. To test the claim, a researcher selected a random sample of 50 gum chewers and found the mean number of sticks of gum chewed per day was 7.5 and the standard deviation was 1.5 At = 0.05, is the number of sticks of gum a person chews per day actually greater than 7? Solve Problem2 in the following steps (Write your solution explicitly) a. Write the null Ho and alternative hypotheses H1 b) What is the required conditions (Assumptions) c) Find Test statistic t and P-value (from the Mega-Stat) t = P-value = d) Test the hypothesis is (a) using P-value e) Find Critical value of the statistical test in part (a), at = 0.05 df = Critical value = f) Test the hypothesis is (a) using Test statistic t g) Write the decision in statement of the test you did in (d) and (e) and (f) Copy and paste the MegaStat output for problem 2 Problem3 (Use Mega-Stat to answer this question) After the solution copy and paste the Mega-Stat output. 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 Problem3 in the following steps (Write your solution explicitly) a. Write the null Ho and alternative hypotheses H1 b) What is the required conditions (Assumptions) c) Find Test statistic Z and P-value (from the Mega-Stat) Z = P-value = d) Test the hypothesis is (a) using P-value e) Find Critical value for the statistical test in part (a), at = 0.10 Critical value = f) Test the hypothesis is (a) using Test statistic Z g) Write the decision in statement of the test you did in (d) and (f) (write your solution explicitly) Copy and paste the MegaStat output for problem 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 Problem4 in the following steps (Write your solution explicitly) a. Write the null Ho and alternative hypotheses H1 b) What is the required conditions (Assumptions) c) Calculate the value of the test t (Use formula sheet and write your solution explicitly) d) Find Critical value for this statistical test, at the 5% significance level (using the tables) Critical value = e)Test the hypothesis in (a) is using the test statistic method f) Write the decision in statement of the test you did in (e) (write your solution explicitly) g) Estimate 95% confidence of the population mean. (Use formula sheet and write your solution explicitly) U.L. = L.L. = h) Test the hypothesis in (a) is using the confidence interval method (write your solution explicitly) i) Explain what does "a 95% confidence" means. (interpretation) Problem5 (Use the Formula sheet and the Tables to answer this question, You should not use Mega-Stat In order to determine the productivity of newly hired sales men. It is believed that the productivity of the newly hired sales men different from 470 boxes. To test this belief at the 5% significance level. A random sample of 40 sales men has a mean of 450 boxes and a standard deviation of 50 boxes. Hypothesis Test: Mean vs. Hypothesized Value 470.00 hypothesized value 450.00 mean boxes 50.00 std. dev. 7.91 std. error ----- n ----- df ----- t .0156 p-value (two-tailed) ------ confidence interval 90.% lower ------ confidence interval 90.% upper Complete the missing values of above the Mega-Stat output, and use it to solve the following questions: (Write your solution explicitly) a. Write the null Ho and alternative hypotheses H1 b)Verify the assumptions you need to make the test. c) Test the hypothesis is (a) using P-value d) Write the decision in statement of the test you did in (c) e) Find Critical value of the statistical test in part (a), with 5% significance level (using the tables) df = Critical value = f) Calculate the Test statistic t (Use formula sheet and write your solution explicitly) g) Test the hypothesis is (a) using Test statistic t h) Estimate the population mean with 95% confidence (Use formula sheet and write your solution explicitly) U.L. = L.L. = i) Test the hypothesis is (a) using confidence interval method Problem6 (Use the Formula sheet and the Tables to answer this question, You should not use Mega-Stat) For a certain year, a study reports that the percentage of college students using credit cards was 83%. A college dean of student services believe that this is too high for her university, so she randomly selects 400 students and finds that 300 of them use credit cards. At = 0.05, is college dean believe about her university is correct? Solve Problem6 in the following steps (Write your solution explicitly) Hypothesis test for proportion vs hypothesized value Observed Hypothesized 0.75 0.83 p (as decimal) 300/400 332/400 p (as fraction) 300. 332. X 400 400 n 0.0188 std. error ------ z 2.05E-05 p-value (two-tailed) --------- confidence interval 95.% lower --------- confidence interval 95.% upper Complete the missing values of above the Mega-Stat output, and use it to solve the following questions: (Write your solution explicitly) a. Write the null Ho and alternative hypotheses H1 b) Verify the assumptions you need to make the test. c) Test the hypothesis is (a) using P-value d) Write the decision in statement of the test you did in (c) e) Find Critical value of the statistical test in part (a), with 5% significance level (using the tables) df = Critical value = f) Calculate the Test statistic Z (Use formula sheet and write your solution explicitly) g) Test the hypothesis is (a) using Test statistic Z h) Estimate the population mean with 95% confidence (Use formula sheet and write your solution explicitly) U.L. = L.L. = i) Test the hypothesis is (a) using confidence interval method