Question

4) A company manufacturing solar panels wishes to test two new prototypes, A and B. The
panels are installed at 12 sites, and the average hourly energy outputs
are measured for both prototypes. The results of the measurements are summarized in the
following table,
Site 1 2 3 4 5 6 7 8 9 10 11 12
Prototype A 144.2 113.7 129.1 126.9 129.3 108.7 104.4 125.4 121.2 130.9 111.4 123.1
Prototype B 106.6 111.8 110.3 101.3 108.5 112.2 101.9 111.5 107.2 107.7 108.9 105.8
a) Can these two samples be treated as independent? Why or why not?
b) Construct a 95% confidence interval on the difference between the energy outputs.
c) Based on the result of part b), is there an indication that one prototype is better than the
other? If yes, which one?

Answer 1

Answer:

4) A company manufacturing solar panels wishes to test two new prototypes, A and B. The
panels are installed at 12 sites, and the average hourly energy outputs
are measured for both prototypes. The results of the measurements are summarized in the
following table,
Site 1 2 3 4 5 6 7 8 9 10 11 12
Prototype A 144.2 113.7 129.1 126.9 129.3 108.7 104.4 125.4 121.2 130.9 111.4 123.1
Prototype B 106.6 111.8 110.3 101.3 108.5 112.2 101.9 111.5 107.2 107.7 108.9 105.8
a) Can these two samples be treated as independent? Why or why not?

The two samples be treated as dependent because the measurements are paired by site.

b) Construct a 95% confidence interval on the difference between the energy outputs.

Site	PrototypeA	PrototypeB	d=difference(A-B)
1	144.2	106.6	37.6
2	113.7	111.8	1.9
3	129.1	110.3	18.8
4	126.9	101.3	25.6
5	129.3	108.5	20.8
6	108.7	112.2	-3.5
7	104.4	101.9	2.5
8	125.4	111.5	13.9
9	121.2	107.2	14
10	130.9	107.7	23.2
11	111.4	108.9	2.5
12	123.1	105.8	17.3

$CI = \bar d \pm t* \frac {s}{\sqrt{n}}$

Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation	11.9464
Sample Mean	14.55
Sample Size	12
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	3.4486
Degrees of Freedom	11
t Value	2.2010
Interval Half Width	7.5904
Confidence Interval
Interval Lower Limit	6.9596
Interval Upper Limit	22.1404

95% CI for difference = (6.9596, 22.1404)

c) Based on the result of part b), is there an indication that one prototype is better than the
other? If yes, which one?

The 95% CI for difference (6.9596, 22.1404) does not contains 0 value. That is both upper and lower intervals are positive. We infer that the mean difference is significantly different from 0. Therefore we conclude that one prototype is better than the other.