Question
Exercise is an essential component of a healthy lifestyle, and many college students incorporate exercise into their daily routine. One VCU student tracked his exercise
Exercise is an essential component of a healthy lifestyle, and many college students incorporate exercise into their daily routine. One VCU student tracked his exercise routine at the Cary Street Gym for a simple random sample of 30 days. For each of the 30 days he recorded data for the three variables. The data table is below.
Day | Cardio | Length of workout (minutes) | Calories Burned |
1 | IW | 77 | 206 |
2 | R | 80 | 122 |
3 | IW | 110 | 250 |
4 | R | 102 | 115 |
5 | R | 115 | 108 |
6 | R | 61 | 190 |
7 | R | 87 | 170 |
8 | A | 89 | 125 |
9 | IW | 93 | 225 |
10 | R | 107 | 130 |
11 | IW | 110 | 246 |
12 | R | 98 | 156 |
13 | R | 74 | 178 |
14 | R | 45 | 155 |
15 | A | 72 | 134 |
16 | IW | 83 | 308 |
17 | IW | 134 | 392 |
18 | IW | 117 | 280 |
19 | R | 106 | 119 |
20 | R | 57 | 102 |
21 | R | 97 | 159 |
22 | R | 66 | 167 |
23 | A | 62 | 140 |
24 | R | 112 | 178 |
25 | R | 77 | 184 |
26 | IW | 46 | 406 |
27 | IW | 104 | 289 |
28 | A | 92 | 186 |
29 | R | 138 | 144 |
30 | IW | 74 | 277 |
The first variable is the type of cardio chosen that day. This is a qualitative variable with three possible responses: running (denoted R in the data table below); walking on a treadmill with an incline (denoted IW in the data table below); and agility drills (denoted A in the data table below). The second variable is the length of the aerobic portion of the workout, measured in minutes. The third variable is the number of calories burned during the aerobic portion of the workout. Both the second and third variables are quantitative variables.
3. This question uses the quantitative variable length of the workout in minutes.
(a). Construct an appropriate stem-and-leaf plot to graphically display this data.
(b). Calculate the mean, median, range, standard deviation, and interquartile range for this sample of data.
(c). Use the results of parts (a) and (b) to completely describe the distribution of the data.
(d). The goal is to calculate a confidence interval for the mean length of all workouts in which this person participates. Discuss the two assumptions that must be satisfied in order for the confidence interval to be computed, and whether they are satisfied using the data collected.
(e). Calculate and interpret a 95% confidence interval for the mean length of all workouts in which this person participates. Complete the calculation and interpretation even if the assumptions are violated.
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