Question

Samsung manufactures cellphone with an average standby time of 10 hours between charges. The standby time of the cellphone is normally distributed. During the design stage, the quality engineering staff recorded 18 observations of the standby time of the cellphone. Using the observations below, is there evidence that the average standby time of a Samsung cellphones is not 10 hours? Use a level of significance of .05

Observation

Observations	Time
1	10.85
2	11.4
3	10.81
4	10.24
5	10.23
6	9.49
7	9.89
8	10.11
9	10.57
10	11.21
11	10.1
12	11.22
13	10.31
14	11.24
15	9.51
16	10.52
17	9.92
18	8.33

Answer the following question:

1. What is the null and alternative hypothesis to the case above?
2. Copy the data into excel and do an analysis to test the hypothesis
3. What is the conclusion of your analysis? (try to state it in terms of the original problem or question)

Answer 1

Claim : To test whether  the average standby time of a Samsung cellphones is 10 hours or not.

Hpothesis :

Two tailed test.

Test statistic :

where sample mean can be calculate by using excel command

=AVERAGE(number1,[number2],...)

we get   sample mean = = 10.33

and  sample s.d can be calculated by using excel command

=STDEV.S(number1,[number2],...)

we get sample s.d. = s = 0.77

sample size = n = 18

Standard error = E =    

  

we get E = 0.18

Therefor, test statistic is

  

we get Test statistic = t = 1.83

Degrees of freedom = n - 1 = 18-1 = 17

Level of significance =

Pvalue : By using excel command we can calculate the exact pvalue as

Command is = TDIST(x,DF,Tails)

=TDIST(1.83,17,2)

we get Pvalue = 0.084

Decesion Rule : pvalue >    Then we fail to reject Ho

Conclusion : There is insufficient evidence to conclude that the average standby time of a Samsung cellphones is not 10 hours.