# Statistics

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Your name: , Points: out of 25 (Last name) (First name) Please scan your answers along with your work and upload the document to Canvas either in Word or in PDF format. I will not penalize minor rounding errors. Therefore, do not worry about rounding errors. Do show all the work that leads to your answers. Otherwise, you may not get the point. (Q1 to Q3). Suppose a random sample of 10 students was selected from Indiana University. They were given a statistics exam and their scores are as follows. Answer the following questions (Show calculations) (Report your answers up to two decimal points). 55 78 40 70 80 62 88 40 30 68 1. ( ) of 3. Determine the estimate of the standard deviation of the population (Indiana University students’ statistics exam scores) (please note you are to calculate “s” rather than “σ”). 2. ( ) of 3. What are the standard scores (z scores) of 40, 70, and 88? (of course, you need to use the standard deviation score obtained from Question 1) Z40 = Z70 = Z88 = 3. ( ) of 2. Suppose you transform all the given scores (N = 10) into a distribution with a mean of 50 and a standard deviation of 10. What is the transformed score of 40? (Q4 to Q6) Given a distribution of 3,000 numbers that are assumed to be normally distributed with μ=120 and σ=25, use the properties of the normal distribution to determine the following probabilities (P) (Remember 0 ≤ P ≤ 1, do not be confused with percentage; P should be reported up to four decimal points): 4. ( ) of 2. P (selecting a number less than 100). P (X < 100) = 5. ( ) of 2. P (selecting a number between 110 and 125). P (110 < X < 125) = 6. ( ) of 2. P (selecting a number either less than 75 or greater than 160). P (X < 75 or X > 160) = (Q7 to Q8) Using the sampling distribution of the mean for the sample size 144 in the above problems (Q4-Q6) and the properties of the normal distribution, determine the following probabilities (P). 7. ( ) of 3. P (X > 121.4) = 8. ( ) of 3. P (X < 118.2) = Q9. The Epworth Sleepiness Scale (ESS) was designed to measure whether a person is getting enough sleep. The test asks such questions as how likely you are to doze off in a variety of situations, such as watching TV, or at a meeting, or even as a passenger in a car on a long ride. The test is designed to produce a mean score of 7.50. A random sample of college students was selected and the following scores were obtained: 6, 10, 4, 3, 8, 12, 5, 7, 9, 4, 10, 2, 7, 5, 4, 7, 8, 11, 3, 7. Could this sample be representative of a population whose mean is 7.50? Conduct the hypothesis testing (show all the six steps of hypothesis testing) using α = .05 and the two-tailed test. Give the probability statement after the statistical test is done. Hint: Mean of the sample: 6.60, Variance of the sample: 8.147 Grading Criteria for Q9 ( of 5 possible points) 1. ( ) of 1. Are all the steps of hypothesis testing shown? 2. ( ) of 1. Is the test statistic (t ratio) calculated correctly? 3. ( ) of 1. Is the critical value reported correctly? 4. ( ) of 1. Is the decision (rejection or non-rejection of H0) right? 5. ( ) of 1. Is the probability statement correct? Page 1 of 4

Your name: , Points: out of 25 (Last name) (First name) Please scan your answers along with your work and upload the document to Canvas either in Word or in PDF format. I will not penalize minor rounding errors. Therefore, do not worry about rounding errors. Do show all the work that leads to your answers. Otherwise, you may not get the point. (Q1 to Q3). Suppose a random sample of 10 students was selected from Indiana University. They were given a statistics exam and their scores are as follows. Answer the following questions (Show calculations) (Report your answers up to two decimal points). 55 78 40 70 80 62 88 40 30 68 1. ( ) of 3. Determine the estimate of the standard deviation of the population (Indiana University students’ statistics exam scores) (please note you are to calculate “s” rather than “σ”). 2. ( ) of 3. What are the standard scores (z scores) of 40, 70, and 88? (of course, you need to use the standard deviation score obtained from Question 1) Z40 = Z70 = Z88 = 3. ( ) of 2. Suppose you transform all the given scores (N = 10) into a distribution with a mean of 50 and a standard deviation of 10. What is the transformed score of 40? (Q4 to Q6) Given a distribution of 3,000 numbers that are assumed to be normally distributed with μ=120 and σ=25, use the properties of the normal distribution to determine the following probabilities (P) (Remember 0 ≤ P ≤ 1, do not be confused with percentage; P should be reported up to four decimal points): 4. ( ) of 2. P (selecting a number less than 100). P (X < 100) = 5. ( ) of 2. P (selecting a number between 110 and 125). P (110 < X < 125) = 6. ( ) of 2. P (selecting a number either less than 75 or greater than 160). P (X < 75 or X > 160) = (Q7 to Q8) Using the sampling distribution of the mean for the sample size 144 in the above problems (Q4-Q6) and the properties of the normal distribution, determine the following probabilities (P). 7. ( ) of 3. P (X > 121.4) = 8. ( ) of 3. P (X < 118.2) = Q9. The Epworth Sleepiness Scale (ESS) was designed to measure whether a person is getting enough sleep. The test asks such questions as how likely you are to doze off in a variety of situations, such as watching TV, or at a meeting, or even as a passenger in a car on a long ride. The test is designed to produce a mean score of 7.50. A random sample of college students was selected and the following scores were obtained: 6, 10, 4, 3, 8, 12, 5, 7, 9, 4, 10, 2, 7, 5, 4, 7, 8, 11, 3, 7. Could this sample be representative of a population whose mean is 7.50? Conduct the hypothesis testing (show all the six steps of hypothesis testing) using α = .05 and the two-tailed test. Give the probability statement after the statistical test is done. Hint: Mean of the sample: 6.60, Variance of the sample: 8.147 Grading Criteria for Q9 ( of 5 possible points) 1. ( ) of 1. Are all the steps of hypothesis testing shown? 2. ( ) of 1. Is the test statistic (t ratio) calculated correctly? 3. ( ) of 1. Is the critical value reported correctly? 4. ( ) of 1. Is the decision (rejection or non-rejection of H0) right? 5. ( ) of 1. Is the probability statement correct? Page 1 of 4

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