Review Final Exam STAT 190(1)

Review Final Exam STAT 190 Group A Group A contains 20 multiple choice questions from Chapter 1--- Chapter 11. For the short questions, I recommend you to go through each multiple choice homework questions and the materials in the power point slides instruction materials. Group B Group B contains 3-4 questions from Chapter 1--- Chapter 10. For each questions you need to show your work. You will not get credit if you do not show your work . Here are some example of long questions: 1) Ethan and Drew went on a 5-day fishing trip. The number of fish caught and released by two boys each day was as follows: Ethan 1 3 2 4 5 Drew 1 2 1 4 2 a) Find the mean number of fish caught per day by each fisherman. (Answer: 3, 2) b) Compute the standard deviations. Which fisherman has consistence record? (Answer: 1.58, 1.22, Drew) 2) A survey of 11 randomly selected full time students was conducted in the fall 2015 semester. In the survey, the students were asked to disclose their weekly spending on entertainment. The results of the survey are as follows: 2 54 64 33 65 32 21 16 22 39 150 Ascending Data: 2 16 21 22 32 33 39 54 64 65 150 a) Compute Inter Quartile Range(IQR) (Answer: 43) b) Compute the lower fence. (Answer: -43.5) c) Compute upper fence (Answer: 128.5) d) Check the data set for outlier. (Answer: 150 outlier) 3) Determine whether the Los Angeles Angels or the Colorado Rockies had a relatively better run- producing season. The Angels scored 773 runs, play in the American League, where the mean number of runs scored was 677.4, and standard deviation was 51.7 runs. The Rockies scored 755 runs, play in the National League, where the mean number of runs scored was 640, and the standard deviation was 55.9 runs. (Answer: Colorado Rockies)

Hypothesis Test: Question 1: In the US, historically, 40% of registered voters are Republican. Suppose you obtain a simple random sample of 320 registered voters and find 142 registered Republicans. Consider the hypothesis H 0 : p = 0.4 versus H 1 : p > 0.4 . Suppose, z 0.05 = 1.645 . a) Compute the test statistic .(Answer:1.46) b) Compute the critical value and draw a z-distribution with the critical region shaded for α = 0.05. c) Perform the test for α = 0.05 level of significance. Write the conclusion of the test. (Answer: Since the test statistic does not lie on the critical region so we fail to reject null hypothesis. There is not sufficient evidence at 5% level of significance to conclude that the percentage of registered Republican voters is more than 40%. Hypothesis Test: Question 2: Suppose you wish to find out the answer to the age-old question, “Do American prefer Coke or Pepsi?” You conduct a blind taste test in which individuals are randomly asked to drink one of the colas first, followed by the other cola, and then ask to disclose which drink they prefer. Result of your taste test indicate that 53 of 100 individual prefer Pepsi. Conduct the hypothesis H 0 : p = 0.4 versus H 1 : p > 0.4 . Suppose, z 0.05 = 1.645 . a) State null and alternative hypothesis. (Answer: H 0 : p = 0.4 versus H 1 : p > 0.4 ) b) Compute the test statistic . (Answer:2.65) c) Compute the critical value and draw a z-distribution with the critical region shaded for α = 0.05. d) Perform the test for α = 0.05 level of significance. Write the conclusion of the test. (Answer: Since the test statistic lies on the critical region so we reject null hypothesis. There is sufficient evidence at 5% level of significance to conclude that the percentage of Americans who prefer Pepsi is more than 40%. Hypothesis Test: Question 3: To test H 0 : μ = 20 versus H 1 : μ < 20 , a simple random sample of size n=18 is obtained from a population that is known to be normally distributed. − t 0.05 =− 1.74 a) If x = 18.3 and s = 4.3 , compute test statistic. (answer: -1.677) b) Compute the critical value and draw a t-distribution with the critical region shaded for α = 0.05. c) Perform the test for α = 0.05 level of significance. Write the conclusion of the test. (Answer: Since the test statistic does not lie on the critical region so we fail to reject null hypothesis. There is not sufficient evidence at 5% level of significance to conclude that μ < 20 Hypothesis Test: Question 4: To test H 0 : μ = 4.5 versus H 1 : μ > 4.5 , a simple random sample of size n=13 is obtained from a population that is known to be normally distributed. t 0.05 = 1.78 a) If x = 4.9 and s = 1.3 , compute test statistic. (answer: 1.109) b) Compute the critical value and draw a t-distribution with the critical region shaded for α = 0.05. c) Perform the test for α = 0.05 level of significance. Write the conclusion of the test (Answer: Since the test statistic does not lie on the critical region so we fail to reject null hypothesis. There is not sufficient evidence at 5% level of significance to conclude that μ > 4.5 Hypothesis Test: Question 5: To test H 0 : μ = 105 versus H 1 : μ≠ 105 , a simple random sample of size n=35 is obtained from a population that is known to be normally distributed. t 0.025 = 2.03