A researcher examining data on schools finds that the higher the average income of the parents whose children attend a school, the higher is the average achievement test score for all students in the school. What is the unit of analysis of these data? Can the researcher conclude from the data that the higher the income of an individual student’s parents, the better the student’s achievement test score will be? Why or why not?
In: Math
rofessor Moriarty has never taken a formal statistics course; however, he has heard about the bell-shaped curve and has some knowledge of the Empirical Rule for normal distributions. Professor Moriarty teaches as Honors Quantum Physics class in which he grades on the bell curve. He assigns letter grades to his students' tests by assuming a normal distribution and utilizing the Empirical Rule. The Professor reasons that if IQ and SAT scores follow a normal distribution, then his students' scores must do so also. Therefore, upon scoring the tests, he determines the mean and standard deviation for his class. He then uses the Empirical Rule to assign letter grades so that 68% of the students receive a "C," 95% receive "B-D," and 99.7% receive "A-F."
The following test grades occur on the midterm exam for his class: 78 85 93 62 82 76 74 73 91 66 89 88 86 94 65 90 84 92 94 92 82 85 80 77 52 84 78 83
a) You are working as Professor Moriarty's graduate assistant and he has asked that you use the Empirical Rule to determine which of these grades he should assign as "A," "B," "C," "D," and "F." After finding the mean and standard deviation for the midterm grades, give the interval of test scores that will qualify for each letter category. (In other words, what range of scores will earn an "A," "B," and so on?) Also give how many students will earn each letter grade using this grading scheme.
b) Determine the number of students who would receive an "A," "B," "C," "D," and "F" using a standard grading scheme where 90-100 earns an "A," 80-89 earns a "B," 70-79 earns a "C," 65-69 earns a "D," and below 65 earns an "F." Describe this grade distribution and contrast it with the one that results from using the bell curve.
c) As a student of statistics, you have some concerns about Professor Moriarty's use of the normal distribution in this context. Discuss your concerns with your classmates. Why might his practice not be statistically sound? Provide statistical evidence to support your position so that you can justify your argument against this method of grading. (Statistical evidence could include measures of relative position, charts or tables, explanations supported by statistical knowledge or analysis, etc.)
In: Math
Problem 1. A boy has a fever after coming home in the afternoon. His mother thinks that it could be related to the following three possible reasons: A : He plays football in the rain, B : He takes a cold water shower after playing, C : He eats too many ice creams.
(iii) The mother has 80% confidence that her son’s fever is caused by at least one of the three reasons. She further estimates that the probabilities of the three individual reasons are 0.5, 0.5, 0.2 respectively, and she believes that they are pair- wisely independent. Are the three reasons mutually independent?
(iv) Suppose that the mother is 100% sure that her son’s fever is caused by at least one of the three reasons. Moreover, she believes that they are mutually inde- pendent although she doesn’t know the exact probabilities of any of the individual reasons. After a moment’s thought, she tells her son that one of the three reasons must be certain (that is, one of P(A) = 1 or P(B) = 1 or P(C) = 1 must be true)! Should the boy believe his mother’s assertion?
In: Math
A car company claims to only have a carbon dioxide emissions of .7. You think it’s higher. You collect 100 cars and test the carbon dioxide. You find an average of .75 with a sample standard deviation of .1. Perform a test of hypothesis with an alpha of 10%.
In: Math
THE SAMPLE STATISTICS ARE GIVEN BELOW. ASSUME THE POPULATION VARIANCES ARE NOT EQUAL USE a=0.01
n1=18 n2=13
X1= 785 X2=770
S1=40 S2=25
PLEASE NOTE THAT THE X'S HAVE A BAR OVER THEM
In: Math
You ask 6 of your friends how many dogs they have and how many cats they have. You record the data as ordered pairs (0,0), (0,1), (1,1), (2,1), (3,3), (5, 4).
1.Create a scatter plot of the data
2.Draw in an estimate of the least squares regression
3.Calculate the least squares regression line. Write the equation of that line.
In: Math
You are the owner of a publishing firm and you have a new author that you plan to publish. It is an action/espionage novel. You believe that the author has a good book, but it is her first book and you don’t really know what the sales numbers will look like. As such, you want to do a break even analysis to find out how many books you have to sell in order to get back your initial investment.
The book will be published in paperback sized 6”x9”. The initial set up cost for setting up the press for the book is $900 dollars. After the additional cost for setting up the press, each book will cost $2.19 each to make.
In: Math
The average American man consumes 9.8 grams of sodium each day. Suppose that the sodium consumption of American men is normally distributed with a standard deviation of 0.8 grams. Suppose an American man is randomly chosen. Let X = the amount of sodium consumed. Round all numeric answers to 4 decimal places where possible.
a. What is the distribution of X? X ~ N(,)
b. Find the probability that this American man consumes between 10.6 and 11.1 grams of sodium per day.
c. The middle 20% of American men consume between what two weights of sodium?
Low:
High:
In: Math
The scores for a certain test of intelligence are normally distributed with mean 100 and standard deviation Find the 80th percentile of these scores.
Below is the table used, I still cant figure out what the 80% would be here:
Standard Scores and Percentiles
z-score
Percentile
z-score
Percentile
z-score
Percentile
z-score
Percentile
minus−3.5
00.02
minus−1.00
15.87
0.00
50.00
1.1
86.43
minus−3.0
00.13
minus−0.95
17.11
0.05
51.99
1.2
88.49
minus−2.9
00.19
minus−0.90
18.41
0.10
53.98
1.3
90.32
minus−2.8
00.26
minus−0.85
19.77
0.15
55.96
1.4
91.92
minus−2.7
00.35
minus−0.80
21.19
0.20
57.93
1.5
93.32
minus−2.6
00.47
minus−0.75
22.66
0.25
59.87
1.6
94.52
minus−2.5
00.62
minus−0.70
24.20
0.30
61.79
1.7
95.54
minus−2.4
00.82
minus−0.65
25.78
0.35
63.68
1.8
96.41
minus−2.3
01.07
minus−0.60
27.43
0.40
65.54
1.9
97.13
minus−2.2
01.39
minus−0.55
29.12
0.45
67.36
2.0
97.72
minus−2.1
01.79
minus−0.50
30.85
0.50
69.15
2.1
98.21
minus−2.0
02.28
minus−0.45
32.64
0.55
70.88
2.2
98.61
minus−1.9
02.87
minus−0.40
34.46
0.60
72.57
2.3
98.93
minus−1.8
03.59
minus−0.35
36.32
0.65
74.22
2.4
99.18
minus−1.7
04.46
minus−0.30
38.21
0.70
75.80
2.5
99.38
minus−1.6
05.48
minus−0.25
40.13
0.75
77.34
2.6
99.53
minus−1.5
06.68
minus−0.20
42.07
0.80
78.81
2.7
99.65
minus−1.4
08.08
minus−0.15
44.04
0.85
80.23
2.8
99.74
minus−1.3
09.68
minus−0.10
46.02
0.90
81.59
2.9
99.81
minus−1.2
11.51
minus−0.05
48.01
0.95
82.89
3.0
99.87
minus−1.1
13.57
minus−0.00
50.00
1.00
84.13
3.5
99.98
In: Math
A city has 10,000 households, and you have collected a simple random sample size of 25 from the households in this city and measured how much each household paid in school taxes in 2012. For this sample, X = $2500, and s = $ 1000. You wish to construct a 95% confidence interval for μ.
In: Math
7. Dave’s Pizza periodically has a special week-long sale. As part of the advertising campaign Dave’s
runs one or more television commercials during the weekend preceding the sale. Data from a sample of
4 previous sales are shown.
Number of Ads
Weekly Revenue
12
27600
5
13385
9
15486
15
2820
Estimate the slope and intercept for the number of ads and weekly revenue for Dave’s Pizza. (5 points)
Estimate weekly revenue if 17 ads are placed. Explain your answer. (3 points)
how would you answer these questions
In: Math
In: Math
How many permutations of the letters m, n, o, p, q contain the string mn or the string mo or the string op-last year exam?
In: Math
The first few problems ask you to "describe" a random variable, which means:
Give the sample space S (the result of the random experiment, from which the output of the random variable is calculated);
Give RX (you may schematize it if it is very complicated or infinite);
Give fX (you may use fractions or decimals) and show how it was calculated unless it is very simple;
Problem 2:
Suppose we have a sack with 2 red balls and 5 black balls, and we draw balls without replacement until a red ball is drawn. Let X = "the number of balls drawn".
Describe the random variable XX.
In: Math
One measure of the state of the economy is the amount of money homeowners pay on their mortgage each month. To determine the extent of change between this year and 5 years ago, a random sample of 150 homeowners was drawn. The monthly mortgage payments for each homeowner for both this year and 5 years ago were recorded. Can we infer that mortgage payments, on average, have risen over the past 5 years?
State the appropriate hypotheses and decision rule, (use a .05 significance level)
|
This Year |
5 years ago |
|
613.21 |
783.31 |
|
551.66 |
498.33 |
|
633.4 |
560.8 |
|
703.02 |
745.84 |
|
1158.98 |
1135.76 |
|
1203.77 |
1342.59 |
|
958.4 |
1003.81 |
|
872.57 |
874.24 |
|
1086.69 |
886.97 |
|
692.15 |
760.52 |
|
785.58 |
819.59 |
|
1196.76 |
1127.73 |
|
705.87 |
614.28 |
|
380.99 |
318.21 |
|
964.1 |
769.98 |
|
1025.34 |
1030.62 |
|
726.33 |
593.46 |
|
700.16 |
731.64 |
|
847.21 |
885.72 |
|
767.43 |
813.06 |
|
858.47 |
732.88 |
|
966.11 |
922.84 |
|
501.64 |
428.1 |
|
921.37 |
801.76 |
|
747.42 |
558.12 |
|
993.44 |
1044.33 |
|
872.8 |
814.49 |
|
1006.41 |
981.71 |
|
957.56 |
862.93 |
|
927.7 |
981.66 |
|
791.51 |
829.34 |
|
926.52 |
937.86 |
|
916.45 |
1022.83 |
|
790.54 |
749.18 |
|
1026.06 |
1053.49 |
|
1071.33 |
1046.71 |
|
954.09 |
838.61 |
|
823.69 |
966.36 |
|
973.28 |
901.78 |
|
851.19 |
879.88 |
|
829.46 |
705.31 |
|
845.07 |
597.36 |
|
1150.59 |
817.73 |
|
865.7 |
687.39 |
|
992.31 |
1136.48 |
|
1105.74 |
1162.46 |
|
1098.17 |
1056.31 |
|
949.96 |
971.49 |
|
832.38 |
723.45 |
|
706.99 |
579.4 |
|
776.6 |
712.53 |
|
914.53 |
919.6 |
|
950.93 |
1000.64 |
|
844.96 |
943.07 |
|
1272.33 |
1177.34 |
|
1193.77 |
1260.44 |
|
1192.95 |
1029.59 |
|
889.18 |
932.37 |
|
785.99 |
891.97 |
|
794.99 |
786.56 |
|
1420.67 |
1359.69 |
|
769.54 |
716.6 |
|
905 |
1051.43 |
|
937.82 |
771.66 |
|
837.85 |
691.59 |
|
830.56 |
862.17 |
|
1006.75 |
1011.87 |
|
1014.53 |
970.39 |
|
859.22 |
740.95 |
|
844.19 |
837.66 |
|
653.69 |
713.55 |
|
1036.43 |
1083.54 |
|
936.32 |
993.66 |
|
1067.83 |
934.16 |
|
785.78 |
734.07 |
|
1289.97 |
1203.78 |
|
1019.45 |
1084 |
|
1154.34 |
1220.97 |
|
766 |
849.81 |
|
1064.63 |
1065.69 |
|
1107.34 |
986.74 |
|
1135.39 |
1038.17 |
|
969.32 |
924.85 |
|
679.52 |
759.79 |
|
1306.65 |
1319.13 |
|
882.13 |
703.69 |
|
1156.16 |
1285.66 |
|
1058.55 |
1130.93 |
|
987.55 |
901.81 |
|
1001.2 |
999.7 |
|
1015.94 |
1183.06 |
|
1071.57 |
1192.89 |
|
873.11 |
831.75 |
|
643.56 |
577.35 |
|
1056.94 |
903.02 |
|
882.3 |
967.83 |
|
1006.83 |
1101.75 |
|
835.93 |
857.67 |
|
1161.75 |
1224.46 |
|
1031.69 |
1102.14 |
|
1078.51 |
1210 |
|
692.49 |
724.34 |
|
820.46 |
824.06 |
|
1016.01 |
969.14 |
|
678.78 |
828.01 |
|
1082.32 |
1095.75 |
|
984.96 |
1006.39 |
|
1267.38 |
1461.02 |
|
1022.35 |
1012.31 |
|
753.21 |
724.78 |
|
915.33 |
959.13 |
|
1051.46 |
979.36 |
|
825.76 |
703.88 |
|
1058.28 |
990.9 |
|
891.43 |
888.71 |
|
768.28 |
882.81 |
|
830.71 |
949.45 |
|
1019.65 |
1041.31 |
|
1075.36 |
998.78 |
|
1043.12 |
929.16 |
|
1070.83 |
1022.38 |
|
1027.89 |
1099.14 |
|
1225.82 |
1170.87 |
|
889.68 |
903.36 |
|
735.47 |
826.83 |
|
727.6 |
588.44 |
|
423.58 |
447.92 |
|
1028.21 |
1188.22 |
|
978.63 |
1132.73 |
|
1249.64 |
1347.06 |
|
651.15 |
623.06 |
|
887.56 |
870.17 |
|
1265.12 |
1217.68 |
|
977.6 |
973.38 |
|
696.85 |
719.89 |
|
1009.77 |
884.88 |
|
1148.88 |
1116.76 |
|
989.87 |
912.95 |
|
1024.76 |
1140.64 |
|
825.51 |
933.2 |
|
1137.11 |
1036.84 |
|
934.07 |
829.58 |
|
1005.67 |
732.09 |
|
1164.36 |
1174.83 |
|
1160.31 |
1231.23 |
|
652.57 |
531.79 |
|
1290.54 |
1257.28 |
|
1184.99 |
1236.76 |
|
1132.33 |
1251.48 |
|
806.46 |
613.17 |
In: Math