Question

A manufacturer is interested in the output voltage of a power supply used in a PC. He takes a random sample of 20 power supplies, and measures the output voltage. The resulting data are shown below:

Power Supply	Voltage
1	4.6
2	5.13
3	5.39
4	5.19
5	4.8
6	4.81
7	4.88
8	5.09
9	5.2
10	4.78
11	4.85
12	5.13
13	4.25
14	4.51
15	5.02
16	5.05
17	5.21
18	4.69
19	5.37
20	4.76

(a)Use bootstrapping (with 5000 bootstrap replications) in order to approximate the probability that if we were to repeat the study, the sample mean voltage for 20 randomly selected power supplies would be between 4.87 and 4.97.

(b)Use bootstrapping (with 5000 bootstrap replications) in order to approximate the probability that if we were to repeat the study, the sample mean voltage for 20 randomly selected power supplies would be larger than 5.

(c)  the engineer were to repeat the study, 90% of the time, he would expect the sample mean to be below what value? Use bootstrapping (with 5000 bootstrap replications) to address this problem.

Answer 1

a) Use bootstrapping (with 5000 bootstrap replications) in order to approximate the probability that if we were to repeat the study,

the sample mean voltage for 20 randomly selected power supplies would be below 4.87 is 0.163

the sample mean voltage for 20 randomly selected power supplies would be above 4.97 is 0.269

Now the sample mean voltage for 20 randomly selected power supplies would be between 4.87 and 4.97 is 1 - (0.163 + 0.269) = 0.568

b) the sample mean voltage for 20 randomly selected power supplies would be larger than 5 is 0.161

c) The engineer were to repeat the study, 90% of the time, he would expect the sample mean to be below what value is 5.019