Week 6 Statistics Qnt 561

Chapt 10 # 42
H0: game length is >= 3.5 hours
Ha: game length is < 3.5 hours

mean = 2.9553 stdev = 0.5596

Get the t test statistic: t = (x-mu)/(stdev/sqrt(N)) t = (2.9553-3.5)/(0.5596/sqrt(17)) t = -4.0133

Get the critical value for df = N-1 = 16, one tail, alpha is 0.05:
-1.7459

Since our test statistic is much lower than the critical value, we reject the null hypothesis. There is enough evidence to conclude that games are shorter than 3.50 hours.

Chapt 11 # 58

The amount of income spent on housing is an important component of the cost of living. The total costs of housing for homeowners might include mortgage payments, property taxes, and utility costs (water, heat, electricity). An economist selected a sample of 20 homeowners in New England and then calculated these total housing costs as a percent of monthly income, five years ago and now. The information is reported below. Is it reasonable to conclude the percent is less now than five years ago?

Home Owner Five years ago Now
1 17% 10%
2 20 39
3 29 37
4 43 27
5 36 12
6 43 41
7 45 24
8 19 26
9 49 28
10 49 26
11 35% 32%
12 16 32
13 23 21
14 33 12
15 44 40
16 44 42
17 28 22
18 29 19
19 39 35
20 22 12

SOLUTION

Before After
1 17 10
2 20 39
3 29 37
4 43 27
5 36 12
6 43 41
7 45 24
8 19 26
9 49 28
10 49 26
11 35 32
12 16 32
13 23 21
14 33 12
15 44 40
16 44 42
17 28 22
18 29 19
19 39 35
20 22 12

Since these are before and after measurements, we need to treat this as a paired t-test.

Here 's how the test statistic is calculated.

First we find the different of the samples. I 'll subtract the afters from the befores. Here is the column of differences:

7
-19
-8
16
24
2
21
-7
21
23
3