Data for 4.140 Coffees Temperature 17988 40 13995 52 36330 33 43604 33 33938 40
ID: 3068381 • Letter: D
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Data for 4.140
Coffees Temperature 17988 40 13995 52 36330 33 43604 33 33938 40 18920 54 39957 35 3647 52 25795 29 30049 30 39804 36 25127 42 52633 2 52515 15 41819 49 6383 42 32602 51 26664 28 31271 29 62729 -10 23767 51 22653 52 34502 20 13239 66 34526 15 38300 40 23357 37 18765 41 47408 -5 32758 17 22291 33 20991 39 35818 45 32341 28 43752 31 34836 38 20341 47 26430 31 42780 28 11606 55 23726 37 37023 18 13298 51 26302 35 38279 26 21180 61 38556 5 23228 50 37477 26 20339 54 Coffees Temperature 17988 40 13995 52 36330 33 43604 33 33938 40 18920 54 39957 35 3647 52 25795 29 30049 30 39804 36 25127 42 52633 2 52515 15 41819 49 6383 42 32602 51 26664 28 31271 29 62729 -10 23767 51 22653 52 34502 20 13239 66 34526 15 38300 40 23357 37 18765 41 47408 -5 32758 17 22291 33 20991 39 35818 45 32341 28 43752 31 34836 38 20341 47 26430 31 42780 28 11606 55 23726 37 37023 18 13298 51 26302 35 38279 26 21180 61 38556 5 23228 50 37477 26 20339 54 Mean Mode Variance Standard deviation Descriptive statistics Least squares line 108 109 116 Correlation Coefficient of determination 133 HAPTER EXERCISES a. Determine the mean and median. b. Determine the variance and standard deviatien c. Briefly describe what you have learned from 139 Osteoporosis is a condition in which bone density decreases, often resulting in broken bones. Bone density usually peaks at age 30 and decreases thereafter. To understand more aboat the condition, a random sample of women aged 50 years and over was recruited. Each woman's bone density loss was recorded. a. Compute the mean and median of these data. b. Compute the standard deviation of the bone your statistical analysis. 4.141 Refer to Exercise 4.139. In addition to the Exercise 4 ition to the bn r was receruited. Each womans density losses, the ages of the women were ae recorded. Compute the coefficient of determinai and describe what this statistic tells you. 4.142 Refer to Exercise 4.140. Suppose that in additie density losses. c. Describe what you have learned from the to recording the coffee sales, the manager a recorded the average temperature (measured i degrees Fahrenheit) during the game. These dau together with the number of cups of coffee sll were recorded. a. Compute the coefficient of determination. b. Determine the coefficients of the least squares statistics 140 4 140 The temperature in December in Buffalo, New York, is often below 40 degrees Fahrenheit (4 degrees Celsius). Not surprisingly when the National Football League Buffalo Bills play at home in December, coffee is a popular item at the concession stand. The concession manager would like to acquire more information so that he can manage inventories more efficiently. The num ber of cups of coffee sold during 50 games played in December in Buffalo was recorded line. c. What have you learned from the statistics calculated in parts a and b about the relationship between the number of cupsof coffee sold and the temperature?
Explanation / Answer
(4.140) (a) Mean = 29912.78, Median = 30660.
(b) Variance = 148213791, SD = 12174.309
(c) We see that, on average, 30000 cups of coffee has been sold. There is no outlier values in the data set, because the mean and median values are quite close to each other. Also, the data are a bit left-skewed since the mean value is slightly lesser than the median value. From the SD, we can say that, on average, the number of cups sold lies within 12174 units of the mean value, that is, 30000 cups.
(4.142) (a) Coefficient of determination = 0.5489.
(b) Let y = number of cups of coffee sold and x = temperature. The least squares line is given by: y = b0 + b1x.
Now, b1 = Cov(x,y) / Var(x) = -553.7
b0 = Mean(y) - (b1 * Mean(x)) = 49336.59
The least squares line: y = 49336.59 - 553.7x
(c) From this, we learn that the two variables are linearly related, but the relation is negative, since the slope value has come out to be negative. This means that as the temperature increases, the number of cups of coffee sold decreases and vice versa. The fit of the least squares line is moderate, since the coefficient of determination is close to 0.50.
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