Q1: Unordered (original data)
|
Student ID |
Distance to Work (whole miles) |
|
1 |
31 |
|
2 |
11 |
|
3 |
7 |
|
4 |
18 |
|
5 |
0 |
|
6 |
20 |
|
7 |
14 |
|
8 |
0 |
|
9 |
10 |
|
10 |
12 |
|
11 |
17 |
|
12 |
13 |
|
13 |
33 |
|
14 |
15 |
|
15 |
20 |
|
16 |
5 |
|
17 |
43 |
|
18 |
5 |
|
19 |
24 |
Q2: Ordered Data
|
Student ID |
Distance to Work (whole miles) |
|
5 |
0 |
|
8 |
0 |
|
16 |
5 |
|
18 |
5 |
|
3 |
7 |
|
9 |
10 |
|
2 |
11 |
|
10 |
12 |
|
12 |
13 |
|
7 |
14 |
|
14 |
15 |
|
11 |
17 |
|
4 |
18 |
|
6 |
20 |
|
15 |
20 |
|
19 |
24 |
|
1 |
31 |
|
13 |
33 |
|
17 |
43 |
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Q3: Calculated z-scores associated with each student
In calculating the z-scores, this formula was used; z = (x - µ)/δ. Where x = sample item (mile), δ= 11.23, µ= 24. Below are the z-scores
|
Student ID |
z-scores |
|
5 |
-2.14 |
|
8 |
-2.14 |
|
16 |
-1.69 |
|
18 |
-1.69 |
|
3 |
-1.51 |
|
9 |
-1.25 |
|
2 |
-1.16 |
|
10 |
-1.07 |
|
12 |
-0.98 |
|
7 |
-0.89 |
|
14 |
-0.80 |
|
11 |
-0.62 |
|
4 |
-0.53 |
|
6 |
-0.36 |
|
15 |
-0.36 |
|
19 |
0.00 |
|
1 |
0.62 |
|
13 |
0.80 |
|
17 |
1.69 |
Q4: Identify potential outliers and explain your reasoning
Based on the data, There are no significant potential outliers, except the value 43. The box plot below shows the value.
Q5: 95% and 99% CI using Sample of 4
To calculate CI, the z-score table values for 95%, i.e., 1.96 and for 99%, i.e., 2.58 were used
| 95% CI |
27.07 |
Lower bound |
|
6.43 |
Upper bound | |
| 99% CI |
30.31 |
Upper bound |
|
3.19 |
Lower bound |
As shown above, the CI for the 99% is wider than the CI for 95%. Therefore, the upper bound for 99% CI is 30.31 to 3.19 for the lower bound.
Q6: 95% CI for sample of 7 and 95% for same mean and SD, but with 20 size.
| 95% CI, n = 7 |
21.80 |
Upper bound | |
|
7.06 |
Lower bound | ||
| 95% CI, n = 20 | |||
|
18.79 |
Upper bound | ||
|
10.07 |
Lower bound | ||
The CI for seven samples is smaller than that of a 20 sample, based on the same mean and standard deviation. Therefore, increasing the sample size, despite having the same mean and standard deviation, as shown above, leads to a smaller confidence interval range. For example, in using n = 20, the upper bound is decreased to that of 18.79, while the lower bound is 10.07, which is higher than with the sample of 7 items.
