Midterm Review Part 1 Statistics

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Collin County Community College District *

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1342

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Statistics

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Apr 3, 2024

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Midterm Review Part 1 Statistics 1. Blood glucose levels for obese patients have a mean of 100 with a standard deviation of 15. A researcher thinks that a diet high in raw cornstarch will have an effect on blood glucose levels. 30 obese patients were randomly selected and they followed the raw cornstarch diet. The mean glucose level of these patients was recorded as 140. The researcher concluded with 5% significance that the mean glucose level was significantly different for the group on the raw cornstarch diet. a. Is the first sentence reporting population or sample data? i. Who is in this group? ii. Are the numbers parameters or statistics? iii. Place the proper symbols on all numbers in the first sentence. b. What is the research question? Is the third sentence reporting population or sample data? i. Who is in this group? ii. Is the number a parameter or a statistic? iii. Place the proper symbol on this number. c. Is the fourth sentence reporting population or sample data? i. Who is in this group? ii. Is the number a parameter or a statistic? iii. Place the proper symbol on this number. d. Is the fourth sentence reporting descriptive or inferential statistics? Explain. 2. A researcher hypothesizes that newborn babies are more likely to be boys than girls. A random sample found 13,173 boys were born among 25,468 newborn children. The researcher reports that with 99% confidence, the proportion of newborns that are boys is between 0.509 and 0.525. a. What is the research question? b. Is the second sentence reporting population or sample data? i. Who is in this group? ii. Are the numbers parameters or statistics? iii. Place the proper symbols on all numbers in the second sentence. c. One of the researchers calculates 13173 / 25468 = 0.517 . What symbol should the researcher use with this number? Why? d. Is the second sentence reporting descriptive or inferential statistics? Explain. e. Is the third sentence reporting descriptive or inferential statistics? Explain. f. Convert the third sentence to an inequality using the proper notation g. Can the researcher report that newborns are more likely to be boys than girls? 3. Classify each variable as qualitative/quantitative/discrete/continuous as is possible. a. How many newborn babies are boys b. Weights of patients c. Is the patient diabetic or not?

4. Use the histogram to answer the questions. Salaries for random professor positions were recorded and summarized in the graph a. How many salaries were included in the graph? b. What is the relative frequency of the modal class? c. What percentage of salaries were at least $120,000? d. What proportion of salaries were at most 100,000? e. What is the class width? f. What is the midpoint of the modal class? g. Describe the distribution of the data set. h. Which do you expect to be higher, the mean or the median? i. Which measure of center would be best for this data set? j. Which measure of dispersion would be best for this data set? k. Which measure of relative position would be best to use with these data values? 5. Use the histogram to answer the questions. Demographics were collected on various cities. The median age for the city was recorded and summarized in the graph. a. How many cities were included in the graph? b. What is the relative frequency of the modal class? c. What percentage of cities had a median age of at most 30? d. What proportion of cities had a median age of at least 25? e. What is the class width? f. What is the midpoint of the modal class? g. Describe the distribution of the data set. h. Which do you expect to be higher, the mean or the median? i. Which measure of center would be best for this data set? j. Which measure of dispersion would be best for this data set?

k. Which measure of relative position would be best to use with these data values? 6. Use the table to answer the questions. The exit velocity of all the homeruns for one team’s season was recorded and summarized in the table. Exit Velocity(miles/hr) 90-93 94-97 98- 101 102-105 106-109 110-113 f 1 2 8 22 9 2 a. How many homeruns were included in the table? b. What is the relative frequency of the modal class? c. What percentage of homeruns had an exit velocity less than 102 miles/hr? d. What proportion of homeruns had an exit velocity greater than 97 miles/hr? e. What is the class width? f. What is the midpoint of the modal class? g. Describe the distribution of the data set. h. Which do you expect to be higher, the mean or the median? i. Which measure of center would be best for this data set? j. Which measure of dispersion would be best for this data set? k. Which measure of relative position would be best to use with these data values? 7. Give the advanced interpretation for each measure: a. The mean exit velocity was 103.8 miles/hr. b. The median exit velocity was 103.2 miles/hr. c. The interquartile range of the exit velocities was 3 miles/hr. d. The standard deviation of the exit velocities was 3.9 miles/hr. e. The mode for the exit velocities was 104.0 miles/hr. f. The exit velocity of 107.2 miles/hr has a z-score of 0.872. g. The exit velocity of 107.2 miles/hr is at the 80 th percentile. 8. Calculate the mean and median by hand. A Sunday School class has 10 students. The number of pets in each student’s house was recorded. 0 1 3 2 8 0 1 0 2 1 9. Salaries for random professor positions were recorded. The professor’s salaries had the following calculations: Summary statistics Where: "Job Title" = "Professor" Column Std. dev. Unadj. std. dev. All 18441.36 18120.616 Use the computer output to report the standard deviation and variance with proper symbols. 10. The maximum exit velocity of all Professional Baseball players this year was recorded. The exit velocities had the following calculations: Summary statistics Column Variance Unadj. variance Maximu 9.3874322 9.3509052

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Column Variance Unadj. variance m Use the computer output to report the standard deviation and variance with proper symbols. 11. The maximum exit velocities of all Professional Baseball players this year are bell shaped with a mean of 110 miles/hour and a standard deviation of 3 miles/hour. a. What maximum exit velocities are considered usual? b. What approximate percentage of max exit velocities are slower than 104 miles/hr? c. What approximate percentage of max exit velocities are faster than 119 miles/hr? d. If there were 257 players recorded, how many do you expect to have max exit velocities that are faster than 119 miles/hr? e. What approximate proportion of max exit velocities are faster than 107 miles/hr? 12. A game awards points for certain achievements. The game uses two 5-sided dice. If the player rolls a pair of 1’s on these dice, then they receive 10 points. If the player rolls a pair of 5’s on these dice, then they receive 8 points. If the player rolls any other pair on these dice, then they receive 5 points. All other outcomes receive 0 points. The likelihood of rolling any specific pair is 0.04. Find and interpret the expected number of points. 13. The maximum exit velocity of all Professional Baseball players this year was recorded. The exit velocities had the following calculations: Summary statistics Column n Median Min Max Q1 Q3 Mode Maximum 257 109.8 98.5 118.4 108.1 111.7 108.8 a. Use the computer output to calculate the IQR. Interpret this number. b. Use the computer output to calculate both fences and decide if the data set has any outliers. 14. Consider the correlation coefficient r. Specify what each value of r indicates: a. 0 b. 1 c. –1 d. 0.2 e. –0.9 15. A study was done to try and link credit score to the interest rate received on a loan. The following computer results were obtained: Simple linear regression results: Dependent Variable: Interest Rate Independent Variable: Credit Score Interest Rate = 61.36874 - 0.076369166 Credit Score Sample size: 6 R (correlation coefficient) = -0.97587063 R-sq = 0.95232348 Estimate of error standard deviation: 1.4240992

a. What type of relationship exists between the credit scores and the interest rate? b. Use the computer output to report the percentage of explained variation and interpret. c. Use the computer output to test for a linear relationship. Specify the critical value. d. Can we say that higher credit scores cause the interest rate to decrease based solely off of these calculations? 16. What branch of mathematics makes us able to draw conclusions about populations when we only have sample data? 17. State what each symbol represents. If there is more than one possible answer, include all answers. A. x B. ^ p C. σ 2 D. p E. x F. σ G. ρ H . μ I. s J. s 2 K. N L. r M. n 18. A modified box plot is given. Describe the shape of the distribution. Are any of the data values outliers? Describe the position of the data value 60 in the data set (the end of the left whisker is at 60). For this data set, what are the best choices of measurements for center, dispersion, and relative position? What is the expected relationship between the mean and the median? 19. A Regular Box Plot is given. For this data set, Q1=Median. Describe the shape of the distribution. For this data set, what are the best choices of measurements for center, dispersion, and relative position? What is the expected relationship between the mean and the median? Compare the box plot in #3 to the box plot in #4. Which distribution has the least dispersion? Which distribution is the most consistent? 20. What is the only measure of center that may be used with qualitative data? 21. Which measure/s of center suffer from a massive loss of information? Which measure/s of center may be used with qualitative data? Which measure/s of dispersion suffer from a massive loss of information? Which measure/s of dispersion are resistant? 22. How can a measure be tested for resistance? 23. Name 3 measures of center. Name 4 measures of dispersion. Name 3 measures of relative position.

24. What must be true if the dispersion of a data set is 0? 25. The mean of the z-scores is always ______________. The standard deviation of the z-scores is always ________________. What z-scores indicate unusual data values? 26. The GRE is an exam that some students need to take before Graduate School. The mean score on the verbal section of the GRE is 150 points, with a standard deviation of 8 points. The analytical writing section of the GRE has a mean of 3.5 and a standard deviation of 0.6. Gerhard took the GRE and scored 145 points on the verbal section and 3 points on the writing section. On which section did he perform relatively better? Gerhard scored 160 points on the quantitative portion of the GRE. Interpret the fact that this score of 160 was at the third quartile. 27. Sketch each of the 4 shapes we have learned for distributions. 28. A class of 60 students took a science quiz with 5 questions. 24 students scored a 100, 35 students scored an 80, and the remaining students all scored a 60. Find the average grade on the quiz. 29. Decide about the strength and direction of the relationship between the variables by inspecting the scatterplot. Approximate the value of r for each graph. 30. In the linear equation y = 3 − 2 x , what is the slope? What is the y-intercept? 31. A motorcycle shop wants to know if the number of parts ordered is related to the number of calls that they receive. What variable should be explanatory, and what variable should be the response? 32. Is the correlation coefficient resistant? What does this mean to you as a researcher? 33. What is the lowest value of the correlation coefficient that will allow us to conclude that a significant linear relationship exists when the sample size is 8? 34. Why should you always inspect a scatterplot of the data before running a linear regression? 35. Why is correlation not the same as causation? 36. If n is 7 and r is 0.671, is there a significant linear relationship between the variables? 37. If r is 0.671, what is the percent of explained variation? Interpret this number.

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