Statistics Test - Fall 2023

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Centennial College *

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MATH182

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Statistics

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Feb 20, 2024

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 Hello all, Here are the instructions for your Test: 1. Solve on paper, then type the answers in the boxes provided. 2. Use ONLY the methods discussed/used in classroom instructions. 3. The test consists of 10 questions and you have 120 minutes to complete the test (once you open it). Very important: Please click the Submit button before the expiry of those 120 minutes. Written solutions sent by email will NOT be accepted. 4. Follow instructions on how to type your answer and the number of decimals; if you use a different number of decimals, answer will show incorrect. 5. DO NOT type any variables in the answer box where answer is a number; just type the number. 6. Values of z should be rounded off correctly to 2 decimal places. Values of probabilities and z or t values that do not come from the tables provided on eCentennial will be considered incorrect and marked with zero. 7. You may use your own formula sheet and a calculator. 8. Any other aids will be considered a breach of academic honesty and treated as such. 9. The test will be available for a window of time starting at 8:30 am until 11:59 pm on Friday, October 20. There are no rewrites or extensions of the tests. 10. You will not be able to see your mark after you click Submit. Both quizzes and tests done on eCentennial will be marked by hand. Thank you

Q1 The Speedy Oil Change Company advertised 35 minute wait for an oil change. A sample of 27 oil changes showed a mean time of 34.5 minutes and from previous studies it is known that the population standard deviation is 5.8 minutes. At the 7% level of significance, is there evidence that the mean time for an oil change is less than 35 minutes? Assume the data is normally distributed. Perform the following steps of hypotheses testing and draw a conclusion. 1. State the hypothesis ( Do NOT type the units) Use these symbols >, <, =, ≠ (copy and paste) [1 mark] H 0 : μ minutes H 1 :μ minutes 2. We should use distribution. (fill in the blank using z or t ) [1 mark] 3. Type of test : tailed test (fill in the blank using left , right , or two [1 mark] 4. Find the Critical Value(s) . Use ± if needed. Type just a value. For example, 1.1111 [2.5 marks] Critical value(s) = 5. Calculate and find correctly rounded test statistic or test value. Type only the value. For example, 1.11111 [2.5 marks]

6. Make the decision . [1 mark] Since the test statistics falls under the region (Fill in the blank with these words: acceptance, or critical ), we the null hypothesis. (fill in the blank with these words: reject, or fail to reject ) 7. Summarize the results . [1 mark] Therefore, there is evidence to the given claim. (Fill in the blank with enough or not enough , and support , or reject ) Question 2 (5 points) Saved Listen Tables A survey of 587 students showed that 97 of them purchase books online. a) Find the sample proportion of success rounded to two decimal places. [1 mark] b) Find the critical Value for the 83% confidence interval. Write exact value from the table. [2 marks] c) Find margin of error rounded to three decimal places. For example, 2.222 [1 mark] d) Find a 83% confidence interval estimate of the proportion of all students who purchase books online. Round answers to three decimal

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places and separate the lower and upper limits of the interval with a comma and no space. For example: 11.111,22.222 [1 mark] Question 3 (10 points) Saved Listen Question 3 options: A company using the newly installed automation software claims that the software can correct itself 48% of the times. The quality control manager feels it is different from the claimed value. She presented a report of 950 glitches in which 411 were automatically corrected. Test this hypothesis at the 0.12 significance level. Perform the following steps of hypotheses testing and draw a conclusion. Tables 1. State the hypothesis: (1 mark) Copy and paste the following symbols as needed: >, <, =, ≠ For example, < 999 H o : p H a : p 2. Type of test: (1.5mark) tailed test (fill in the blank using left , right , or two) 3. Find the critical value(s), type only the value: (3 marks) Copy, paste and use ± if needed.

4. Calculate Test statistic or test value, type only the value: (2.5 marks) 5. Make the decision: (1 mark) Since the test statistics falls under the region (Fill in the blank with these words: acceptance , or critical ), we the null hypothesis. (fill in the blank with these words: reject , or fail to reject ) 6.Summarize the results: (1 mark) Therefore, there is evidence to the given claim. (Fill in the blank with enough or not enough , and support , or reject ) Question 4 (6 points) Saved Listen 38 percent of couples who plan to marry this year are planning simple backyard weddings. Assume the variable is binomial. In a random sample of 10 couples who plan to marry, find the probability of the following. Round final answers to three decimal places . a) Exactly 3 couples will have a backyard wedding. [2 marks] b) Less than 3 couples will have a backyard wedding. [2 marks] c) At least 2 couple will have a backyard wedding. [2 marks] Question 5 (3 points) Saved Listen

3. A professor wants to research about correlation between their students' performance and weekly time spent on studies. The professor asked 7 students about how many hours per week they spent on studies and their grades in the last test. Following plot indicates the findings of this survey. Using above chart, answer the following questions. a) Find the value of the coefficient of correlation, rounded to three decimals. [ 1 mark] b) Using this model, if a student spent 5 hours/week on studies, what would be their score on the test, rounded to two decimals? [1 mark] Question 6 (4 points) Saved Listen 4. Determine the expected value and the standard deviation of the following probability distribution. Round final answers to two decimal places. x P(x) 1 0.44 2 0.25 3 0.19 4 0.12 a) Determine the expected value. [2 marks] b) Determine the standard deviation. [2 marks] Question 7 (9 points)

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Saved Listen Question 7 options: The average local cell phone call length was reported to be 7.45 minutes. A random sample of 19 phone calls showed an average of 8.50 minutes in length with a standard deviation of 1.33 minutes. At α= 0.05, can it be concluded that the average local cell phone call length is 7.45 minutes? Assume that the population is approximately normally distributed. Perform the following steps of hypotheses testing and draw a conclusion. Tables 1. State the hypothesis. Use these symbols >, <, =, ≠ (1 mark) Ho: μ minutes Ha:μ minutes 2. We should use distribution. (fill in the blank using z or t) (1 mark) 3. Type of test: tailed test (fill in the blank using left, right, or two (1 mark) 4. Find the critical value(s). Copy, paste and use ± if needed (2 marks) Critical value(s) = 5. Test statistic or test value rounded to three decimal places =

(2 marks) 6. Make the decision. (1 mark) Since the test statistics falls under the region (Fill in the blank with these words: acceptance , or critical ), we the null hypothesis. (fill in the blank with these words: reject , or fail to reject ) 7.Summarize the results. (1 mark) Therefore, there is evidence to the given claim. (Fill in the blank with enough or not enough , and support , or reject ) Question 8 (5 points) Saved Listen Given a sample containing 38 values, find the following: a) The position of the median [1 mark] b) The position of the 39th percentile [1 mark] c) If the interquartile range is 26, with a third quartile of 30, what is the first quartile? [1 mark] d) If the sample standard deviation is 2.3, find the sample variance. Express you answer correct to 2 decimal places if necessary. [1 mark] e) If the data contains 30 different values, and 2 values occurring each four times, how many modes are in the data set? [1 mark]

Question 9 (5 points) Saved Listen A new evaluation scheme is to be introduced to at a college. Usually for a statistics course at that college, the result is normally distributed with mean of 71 and a standard deviation of 9.5. a) If top 2% of students will receive a scholarship of $1000, what is the minimum score required to receive this award? [2.5 marks] Round your final answers to one decimal place. b)The bottom 4% of the students would be considered fail in the course and must repeat the course. What is the minimum score required for a student to avoid repeating the course? Round your final answers to one decimal place. [2.5 marks] Tables Question 10 (3 points) Saved Listen The average lifespan of a type of a deer is 23 years with a standard deviation of 8.2 years. Find the probability that a random sample of 34 deer will have a mean lifespan between 20 and 25 years. [3 marks] Round your final answer to four decimal places.

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