STA_1300_01_Midterm_2__Chapters_5___9_(1)

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California Polytechnic State University, San Luis Obispo *

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1300

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Statistics

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Feb 20, 2024

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pdf

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STA 1300 Midterm 2 October 26, 2020 Name: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . This exam is open-book and open notes, but you can use a scientific/graphing calculator. Please show all your work, and use of formulas. Try not to leave anything blank; I can still score based off of your thought process. Minimal points will be earned if no work is shown. Tips: Write out every formula used for the most points, label any graphs and plots, if question says to explain, use your words. Question 1 2 3 4 5 Online Total Score 20 10 15 20 20 10 95 1

1) [20 points] The BCD News Channel Forecast has determined that there is a 53% chance of rain for this whole week. Note that a week is 7 days. Answer the following. (a) [4 points] Is this a binomial experiment? If it is, list 3 properties it follows. (b) [3 points] What is the probability that all days of the week will rain? (c) [8 points] What is the probability that three days of the week will rain? (c) [5 points] What is the expected value and the standard deviation of this experiment? 2

2) [10 points] Voters: There are 25 students in Mrs. Bush’s freshman class. On a election day in November, the teacher was wondering who is going to vote. After questioning each student, the school counselor constructed the following table. Vote No Vote Male 6 12 Female 4 3 (a) [2 points] Find the probability that a randomly selected student votes. (b) [3 points] Find the probability that a randomly selected student is female or votes. (c) [3 points] Find the probability that a randomly selected student is neither voting nor is a male. (d) [2 points] Find the probability that a randomly selected student is both a voter and a non-voter. 3

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3) [15 points] Jeff is in class A and Jane is in class B. They both take a the same midterm from the same instructor, but Jeff’s class had a score of 73 with mean μ A = 69 . 4 and σ A = 3 . 1 while Jane had a score of 68 with μ B = 63 . 8 and σ B = 2 . 8. (a) [5 points] What is Jack’s z-score in Class A? (b) [3 points] What is Jaime’s z-score in Class B? (c) [2 points] Did Jack do better than Jaime? (d) [5 points] Draw the standard normal curve with the positions of where Jack and Jaime lie. 4

4) [20 points total] You want to find out how fast people peel a banana. A sample of 81 was taken, with a sample mean of 5 seconds, and sample standard deviation of 1 second. Compute a 99% confidence interval for the population mean μ . (a) [2 points] What is your confidence level c ? (b) [3 points] What is the critical value? (c) [5 points] What is the margin of error E ? (d) [5 points] Give the 99% confidence interval. (e) [3 points] Interpret this confidence interval. (f) [2 points] If a scientist conducted a study that shows that μ = 4 . 2, does your confidence interval contradict the scientists population? Why? 5

5) [20 points] The BCD Times News reported that the mean of watching Netflix in 2012 was 10 hours per day. A social scientist from RGB News Times wanted to test this. The scientist took a sample of 101 and found that the mean hours watched in the sample was 11.5 hours per day. Assume that the population standard deviation is 7.0. The social scientist wants to know if the population mean of watching Netflix is any different from 10 hours. Use α = 0 . 02 and the P-Value Method. (a) [4 points] State your hypotheses: H 0 : H 1 : (b) [1 point] What kind of testing is this? (Left, right, or two-tailed) (c) [5 points] Using the information from the passage, compute the test statistic: (d) [5 points] Compute the P-Value. (e) [3 points] What is your conclusion? (f) [2 points] Interprest the conclusion in reference to the passage. 6

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