Summer 2017 Exam 1 Key
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Austin Peay State University *
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GEOG-306
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Mathematics
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Jun 26, 2024
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Math 1530: Elements of Statistics EXAM I NAM INSTRUCTIONS: J ' Vz} 1. You may use a calculator, #2 pencils) one page of notes) and yqur brain. You mayfi»v aT share any materials and you MUST do your own work to receive any credit. 2. Record all your answers on the scantron bubble sheet. 3. Ask your proctor if you have any questions at all. Good luck! Special Code:‘ 777190 5
N1 «M’S)\)\efiffi A A ((}(’ { aep- 1. Outcomes of the __________ variable depend on values of the __________ va,r1ab (‘A /U\&'Q (a) lurking; response (b) response; lurking (c) explanatory; response response expla ory 2. The time it takes to fill a tub of water is RV variable. (a) quantitative discrete ‘ quantitative continuous (c) categorical 3. 'The number of cats in a cradleisa .. variable. ; uantitative discrete (b) quantitative continuous (c) categorical 4. The make and model of acarisa variable. (a) quantitative discrete (b) quantitative continuous @ategorical 5. ZFhe number of cars in the parking lot is yuantitative discrete (b) quantitative continuous (c) categorical Which of the following statements are true, and which are false? Mark (a) for true and (b) for false. 6. The standard deviation measures how far the data tend to be from the ¥de. Mten = 7. Jack’s test score was at the 30th percentile and Jill’s was at the 65th percentile. This means about of the scores fell between Jack’s and Jill’s scares. Beds e b ol s (m%fl ?Q% 8. A z-score tells the direction and number of r??@n%\bwm%andawmfl‘ 9. The median lies to the xight of the mean for a right-skewed distribution. /\' 10. The regression line has the property that the sum of the squared errors (or sum &%cfiared residuals) is as small as possible. 12. About 95.45% of a population with a bell-shaped distribution Jieg within yé st '%n of Ms¥ the mean. o { 25% ’qu 4 &(‘ 13. Approximately 7%% of a population are above the third quar , ’L?Zl -» S’[o 14. Influential observations tend to lie far from most of the other data points, and they can have a large influence on the slope of the regression line. 11. The third quartile divides a data set into a lower 75% and upper 25%. l 15. The more spread out data are f‘sor% their mean, the larger the standard deviation 15, 16. Data with an r value of 0.09 are%strongly correlated. e—re—0 17. Two data sets with the same mean should have approximately the same standard deviation. 18. If the @!:%lation between two quantitative variables if -0.99,| the variables have a strong linear relationship. e
Use the following information to answer questions on this page. Lightbulb'L ifetimes by Brand - ' b 4 T T T w el a0 w0 T oaw 20 20 20 ‘HS Lightbulb Lifetimes (hours) 19. What would be the most appropriate description for Brand B’s distribution? (a) Left-skewed ight-skewed (c) Symmetrical ~ (d) J-shaped (e) Uniform 20. Which brand had the lowest median life — L '\9\1@ (d) Brand B VN c) 24 (d) Brand A 22. mtawas the minimum lifetime for Brand A? @ (b) 201 , (¢) 213 (d) 237 (e) 257 23 . Which of the following is true? (a) 213 (b) 151 21. Which brand had the largest spread? —— n— (a) 76 - (b) 98 a) About 25% of Brand A bulbs lasted more than 201 hours. About 25% of Brand C' bulbs lasted more than 143 hours. (c) About 75% of Brand B bulbs lasted more than 128 hours. (d) About 50% of Brand A bulbs lasted less than 190 hours. (e) Brand A had a smaller range than Brand C.
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24. 25. 26. 27. 28. The questions on this page refer to the histogram below showing the numbers of different jobs that some undergraduate students had while in college. Numbers Jobs of Jobs for College Students k e ,‘\ ; = c/...l) v %&3 : How many students-tgd)at leas M jobs 3 (a) 0 (c) 4 (d) 5 @ What shape best describes this distribution? /l /l (a) bell-shaped (b) left-skewed @ght—skewed (d) uniform /] 1moé% . What percentage of students had 3 or fewer jobs? 2 / v (a) 0% (b) 14.29% (c) 42.86% b (e) 12 What percentage of the students had ) (c) 16. 67% (d) 42.86% (c) 2 ‘ (d) 2.4444 (e) impossible to tell %{5 4]+ & 2424242 Fury ¢S54 L FT (a) 0% (b) 14.29% What is the average number of jobs? (s .1429 1 o +to te SR— §¢ e = iZ’\Lx
N The data below are the final exam scores = ndomly selected history students and the numbers of hours they slept the night before the éxam. L.i % |HoursofSleep| 3 |5 |2 |8 |2]|4|6]3 L‘)__ Exam Score | 65|80 | 60| 88|66 | 78|90 | 99 A researcher wishes to predict scores based on number of hours. " s g agponse variable? Score (c) History Student (d) History Exam (e) Fear Itself 29. For this study, what is 4 (a) Hours of Sleep ation coefficient r? (c) 68.27% (d) 95.45% (e) 99.73% 30. What is the value of A (a) 33.9% (b) 58.2% 31. The correlation coeflicient = that you calculated in the previous part indicates (a) a strong positive linéar relationship between the variables. (b) a strong negative linear relationship. moderate or weak positive linear relationship. (d) a moderate or weak negative linear relationship. (’L (e) no linear relationship. 32. According to this regression model, what is the percentage of the variation in the variable Scores ot ean be predicted using Hours in the model? ) @' (b) 58.2% (c) 68.27% (d) 95.45% (e) 99.73% 33. If you had to choose exactly one data point moutlier, which would it be? (a) (2, 60) (b) (2,66) () (8, 83) 34. Use the regression line model to predict the € when the numbepetl (a) 33.8 (b) 58.2 (c) 62.5 (e) 95.45 35. Should this model be used to predict the score when the number MNO, because most people do not actually sleep 12 hours. }é\—No, because this results in an exam score of 754, which is impossible. /X - % %\%}l‘g S N T e s (d) Yes, because regression models are always accurate. 0, because this would be extrapolation. 36. ssible lurking variable for this model is lime spent studying (b) height (c) eye color (d) hat size (e) price of eggs 37. What happens when you remove the observation i‘ {rom the data set? (a) The average exam score increases. }{The average hours of sleep decreases. }(Fhe value of r? decreases to 15%. he value of 72 increases to 85%. (e) The equation of the regression line does not change.
The weight of a bouquet of a dozen roses has a bell-shaped distribution with mean 30 oz and standard deviation 2 oz. Use this to answer the next three questions. 38. One bouquet had a z-score 0@;2_5' Which is correct? (a) This bouquet is 3.25 oz below the mean. (b) This bouquet is 3.25 standard deviations above the mean. 71\" (u" L'g 58 ,; RS (c) This bouquet could be considered to be an outlier because its weight is way above average. This bouquet could be considered to be an outlier because its weight is way below average. (e) This bouquet is about average in weight. 39. Approximately what percentage of all bouquets fall between 26 and 34 o (2) 50% (b) 68.27% - (c) 88% (a) 95.45 (b) 100 (c) 150 41. Match the 7 values to the following scatterplots. - (2) (i) 7 = —0.85 (ii) r = —0.98 (iii) 7 = 0.83 (iv) 7 = 0.04 TN (i) r = —0.98 (iif) r = —0.85 ) 7 =004 (i) r=-08 (ii)r=-98 (iv)r=08 T (ii) r = —0.98 (i) r =085 . () 7=083 (e) (i) r = 0.04 (ii) r = —0.98 (iii) 7 = 0.83 (v)r=-085
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R )oY =0 (O (M—-z\ e 42. Yesterday I recorded ten data values. The mean of those values was 20. Today I realized the data value of 40 should have 50. What is the actual mean? (a) 20 (b) (c) 22 (d) 40 (e) 50 43. Tp_general, what effect does increasing the value of one data point have on the mean? creases (b) decreases (c) stays the same (d) goes to France 44, What effect does increasing the W&L value have on the standard deviation? increases (b) decreases (c) stays the same (d) nunya biznass The demand for ham sandwiches each day for eight consecutive days was vax 16 19 25 24 26 22 44 Use this information to answer the following four questions. (c) 245 (d) 25 (c) 5698 (d) 7.87 @ ’ (d)25 (e) 25.5 45. What is the mean? (a) 22 (b) 24 46. What is the sample standard deviation? (a) 28 (b) 5697 4'7. What is the median? (a) 22 (b) 24 48. Whess the range? yl- (G = 2D () ) 49. What is the interquartile resage (IQR)? ) o 28 N fl)& A A (c) 24.5 (d) 7.87 (e) 8.42 Q- Q, =22-20.5 =CS (c) 16 (d) 44 (e) oink! 50. If you had to choose exactly one of the eight data values to be an outlier, which would it be? Use the 1.5 x IQR rule. (a) 16 (b) 22 (c) 25.5 (d) 44 W e A a2 Q, - L.S*1IQR = 205 -1LS%( 634c.Y¥IQP—= 2% +1.S ¥ Y [N “ow -%’K* Bt&u \!\pl.w ie qu‘&()w O.?S,, a..,\() (e) 1,000,000 S = (0.25 3 e.2§ Qr)ut(u./«& @l Mv\ t¢, 34‘&3\5(%(,&_, 3(0 Q’y
: \ < Jack and Jill hired a band to play at their wedding. The band knowgS. gfl ‘ 51. How many different ways can the band arrange all their songs lay in order? (a) 1.2599 x 104 (b) 3.0658 % 10°2 (c) 52 (d) 8)0658 x 1057 (e) 8,675,309 52. If Jack and Jill only need the band to play 20 songs, how many different ways can 20 songs be chosen &52? That is, how many different subsets of size 20 are there? T (a) /9599 x 1014< (b) 3.0653 x 1052 (c) 52 (d) 8.0658 x 1057 () 8,675,30 wl ¢« 20 the 20 songs be chosen from the 52 arlc_l_‘lia_}ied in order? (b) 34653 x 103 (c) 52 () 8.0658 x 1067 (c) 8,675,309 gl uP « LO T < 53. How many different wa; (a) 1.2599 x 10 Determine whether each scenario is an observational study or an experimental design. 54. The band at Jack’s and Jill’s weddmg wants to study the effects of what songs they play on whether or not people dance. They decide to play five songs from each of these categorles R&B, Country, Death Metal, Rap. Whileseach song is played, the bass player counts the people who dance. — am— (a) observational stud @» perimental design 55. The wedding coordinator wonders if booze sales at the wedding are positively associated with the number of people who dance. Each time the band starts a new song, she counts how many people dance and tallies iow much booze is sold. , observational study (b) experimental design 56. The wedding coordinator wonders about the effect of cooking temperatlire on how fnany pedple get sick. She prepares duck according to three different temperatures, and randomly serves the different kinds to people who request duck. She counts the peopte—who get sick from each of the three temperatures and compares. - : @“‘3 7% ‘H‘G‘H L\{ uueM-,. (a) observational study perimental design 57. Jack and Jill are concerned because many of their guests (1) have food poisoning, (2) have had too much to drink, or (3) are dancing like maniacs. They count how many are in each category and make a_pie chart to put in their wedding book. servational study (b) experimental design 58. Jack invited 44 guests, but only 22 attended the ceremony. Jill invited 500 guests, but only 250 attended the ceremony. Is there an association between the person (Jack or Jill) and the percentage gn- 20 ofavitees that attend? G S0 _ ¢ 0, because 22/44 = 250/500. R (U o (b) No, because 22 is much less than 250. Yle __& s %w (c) Yes, because 22/44 = 250/500. o os ‘;J):{., - ij ' (d) Yes, because 22 is much less than 250. 6 3 @f; $ ;k\§ >~ (e) Yes, because 44 is much less than 500 (Jill has more friends to begin with).