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.

4. This question uses the quantitative variable calories burned.

(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). It is hypothesized that the mean number of calories burned during all workouts would be 150 calories, and of interest is to test this hypothesis versus the alternative hypothesis that the mean number of calories burned is different from 150 calories. Write out these two hypothesis in statistical notation.

(e). Discuss the assumptions required to test the hypotheses in part (d) and whether they are satisfied using the data collected.

(f). Use the data to test the hypotheses in part (d) at significance level a = .10. Complete the test even if the assumptions are violated.