Final Exam for Statistics

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Strayer University *

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135

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Statistics

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Jan 9, 2024

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docx

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20/25 that's 80% RETAKE 20 questions were answered correctly . 5 questions were answered incorrectly . 1 Sara wonders what percentage of her students answered at least half of the quiz questions incorrectly. The relative cumulative frequency of students who earned a score of 20 or lower on the quiz is __________ .  34%  14%  28%  68% RATIONALE To get the relative frequency of 20 or lower, we need to find the cumulative number of 20 or less. We simply add up any bin that has the number 20 or less, such as the bin that shows scores of 1-5, 6-10, 11-15, and 16-20. This would be: To get relative frequency, we will take this cumulative number and divide it by the total number of students.

CONCEPT Cumulative Frequency 2 The average number of road accidents that occur on a particular stretch of road during a month is 7. What is the probability of observing exactly three accidents on this stretch of road next month?  0.048  0.023  0.020  0.052 RATIONALE Since we are finding the probability of a given number of events happening in a fixed interval when the events occur independently and the average rate of occurrence is known, we can use the following Poisson distribution formula: The variable k is the given number of occurrences, which in this case, is 3 accidents. The variable λ is the average rate of event occurrences, which in this case, is 7 accidents. CONCEPT Poisson Distribution 3 A survey asked 1,000 people which magazine they preferred, given three choices. The table below breaks the votes down by magazine and age group.

Age Below 40 Age 40 and The National Journal 104 200 Newsday 120 230 The Month 240 106 If a survey is selected at random, what is the probability that the person voted for "Newsday" and is also age 40 or older? Answer choices are rounded to the hundredths place.  0.54  0.66  0.23  0.34 RATIONALE If we want the probability of people who voted for "Newsday" and are also age 40 and over, we just need to look at the box that is associated with both categories, or 230. To calculate the probability, we can use the following formula: CONCEPT Two-Way Tables/Contingency Tables 4 The weekly salaries of full-time and part-time employees at a company are listed on the table. What does the circled section represent?  Sixty-eight full-time employees earn $34 per week.

 Two part-time employees earn between $680 and $690 per week.  Two full-time employees earn more than $680 per week.  Thirty-four part-time employees earn more than $680 per week. RATIONALE If we recall that the stem and leaf can give us the actual values in the data set, then the circle corresponds to $683 and $684. We can then note that there are two part-time workers who make between $680 and $690. CONCEPT Stem-and-Leaf Plots 5 The owner of a new store on Main Street wants to turn the boulevard outside into extra parking spaces because she is concerned about parking availability. She randomly selects 500 residents of the town to take a survey, and these individuals have confirmed their participation. One of the survey questions reads, “Many residents believe the lack of available parking on Main Street is a major problem, and extra spaces along the boulevard would help. Do you agree?" The store owner's survey could suffer from which type of bias?  There is no evidence of bias in the way this survey is carried out.  Selection bias  Response bias  Nonresponse bias RATIONALE

By stating that many residents already believe parking is an issue and putting a response inside of the question, this is a good example of response bias. CONCEPT Nonresponse and Response Bias 6 The blood bank at a hospital has 1,200 units of blood, out of which 37% units are of blood group B+. A clinical researcher randomly selects 300 units of blood and finds that 33% of those are of blood group B+. To test his result, he randomly selects 200 units of blood and finds that 40% of those are of blood group B+. Which of the following is the reason there is a difference between the two percentages selected by the researcher?  Both samples suffered from non-response bias.  The samples were not random samples.  The sample sizes were both too small.  Random error; the numbers were different due to variability inherent in sampling. RATIONALE When sampling, there is always some variability that occurs. So, although the sample values are different, since they were randomly chosen, the differences are simply due to the variability that comes from sampling and not due to some systematic bias. CONCEPT Random and Systematic Errors 7 For a set of data, x is the explanatory variable. Its mean is 8.2, and its standard deviation is 1.92. For the same set of data, y is the response variable. Its mean is 13.8, and its standard deviation is 3.03.

The correlation was found to be 0.223. Select the correct slope and y-intercept for the least-squares line. Answer choices are rounded to the hundredths place.  Slope = 0.14 y-intercept = 12.65  Slope = 0.35 y-intercept = 3.37  Slope = 0.35 y-intercept = 10.93  Slope = 0.14 y-intercept = 6.27 RATIONALE We first want to get the slope. We can use the formula: To then get the intercept, we can solve for the y-intercept by using the following formula: We know the slope, , and we can use the mean of x and the mean of y for the variables and to solve for the y-intercept, . CONCEPT

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