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Comprehensive Statistical Analysis: Descriptive Statistics, Probability

A solved exam on comprehensive statistical methods, covering descriptive statistics, hypothesis testing, regression, and confidence intervals.

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    Comprehensive Statistical Analysis: Descriptive Statistics, Probability, Hypothesis Testing, Regression, and Confidence Intervals Answer all 30 questions. Make sure your answers are as complete as possible. Show all of your work and reasoning. In particular, when there are calculations involved, you must show how you came up with your answers with critical work and/or necessary tables. Answers that come straight from programs or software packages will not be accepted. Refer to the following table for Questions 1, 2, and 3. The table shows temperatures on the first 12 days of October in a small town in Maryland. Date Temperature Date Temperature Date Temperature Oct 1 73 Oct 5 53 Oct 9 62 Oct 2 66 Oct 6 53 Oct 10 49 Oct 3 66 Oct 7 62 Oct 11 52 Oct 4 70 Oct 8 55 Oct 12 57 1. Determine the five number summary for this data. Put your numbers in order . 49, 52, 53, 53, 55, 57, 62, 62, 66, 66, 70, 73 Find the minimum and maximum . The minimum is 49 and the maximum is 73 Find the median Given d 7 ata is even, take average of two middle values Median= 5 . 59 2 119 2 62 57 = = + Place parentheses around the numbers above and below the median. 49, 52, 53 , 53, 55, 57, 62 , 62, 66, 66 , 70, 73 Q 1 =53 Q 3 =66 Write down your five number summary minimum=1, Q1 = 53 , median= 59.5 , Q3= 66 , and maximum= 73 7. 2. Determine the mean temperature. 8 . 59 12 718 12 73 70 66 66 62 62 57 55 53 53 52 49 = = + + + + + + + + + + + = Mean 3. Determine the mode(s), if any.

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    There are 3 modes in this data, 53, 62, 66 Refer to the following situation for Questions 4, 5, and 6. Consider the following distribution by age groups. Age Frequency Relative Frequency 10 – 14 0.04 15 - 19 20 – 24 10 25 – 29 6 30 – 34 5 35 – 39 4 40 – 44 2 45 – 49 1 Total 50 4. Complete the table. Age Frequency Relative Frequency 10 – 14 0.04*50= 2 0.04 15 - 19 0.40*50= 20 1 - 0.60*= 0.4 0 20 – 24 10 0.2 0 25 – 29 6 0.12 30 – 34 5 0.1 0 35 – 39 4 0.08 40 – 44 2 0.04 45 – 49 1 0.02 Total 50 *0.04+0.20+0.12+0.10+0.08+0.04+0.02=0.60 5. Is the distribution bell - shaped, skewed to the left, or skewed to the right? Explain your answer.

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    0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 1 2 3 4 5 6 7 8 Relative Frequency Skewed to the right: The right tail of the histogram is longer than the left tail . 6. In what age range is the median? Explain your answer. Age Frequency Class Boundary Cumulative Frequency 10 – 14 2 9.5 - 14.5 2 15 - 19 20 14.5 - 19.5 22 20 – 24 10 19.5 - 24.5 32 25 – 29 6 24.5 - 29.5 38 30 – 34 5 29.5 - 34.5 43 35 – 39 4 34.5 - 39.5 47 40 – 44 2 39.5 - 44.5 49 45 – 49 1 44.5 - 49.5 50 Total 50 item item n c n f h l Median th th 25 2 50 2 2 = =             − + = 7. Your entire gold coin collection consists of 5 coins. Their weights are 2, 3, 8, 7, and 6 ounces respectively. Find the standard deviation of their weights. Show all work. Mean = (2+3+8+7+6) / 5 = 26/5 = 5.2 s² = [(2 - 5.2)² + (3 - 5.2)² + (8 - 5.2)² + (7 - 5.2)² + (6 - 5.2)²] / (5 - 1)

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