Question

A technical engineer is interested in understanding the battery life of two different laptops for student usage at a community college in California. The two models he has are Madroid and Krapple. He randomly assigned students to one of the laptop models and recorded the number of minutes the students were able to use the computer until the battery ran out. Below is the data collected.

Student #	Madroid	Krapple
1	540	575
2	380	525
3	420	583
4	480	680
5	530	628
6	467	680
7	465	640
8	498	630
9	482	725
10	309	780
11	609	530
12	504	280
13	590	350
14	403	376
15	602	540

Does the technical engineer have statistically significant evidence to present to the university budget committee to purchase Krapple because it has, on average, a longer battery life?

Provide the p-value from your analysis

Answer 1

Here we have paired data so paired t test should be used.

Let d = Krapple - Madroid

Following table shows the calculations:

Krapple	Madroid	d	(d-mean)^2
575	540	35	2291.5369
525	380	145	3860.1369
583	420	163	6420.8169
680	480	200	13719.4369
628	530	98	228.9169
680	467	213	16933.8169
640	465	175	8487.9369
630	498	132	2413.7569
725	482	243	25641.6169
780	309	471	150644.8969
530	609	-79	26201.8969
280	504	-224	94169.1969
350	590	-240	104245.0369
376	403	-27	12071.4169
540	602	-62	20987.3169
Total		1243	488317.7335

Conclusion: The technical engineer do not have statistically significant evidence to present to the university budget committee to purchase Krapple because it has, on average, a longer battery life.

P-value = 0.0538