A manufacturer of flashlight batteries took a sample of 13 batteries from a day’

Question

A manufacturer of flashlight batteries took a sample of 13 batteries from a day’s production and used them continuously until they failed to work. The life lengths of the batteries, in hours, until they failed were: 342, 426, 317, 545, 264, 451, 1049, 631, 512, 266, 492, 562, and 298.

At the .05 level of significance, is there evidence to suggest that the mean life length of the batteries produced by this manufacturer is more than 400 hours?

A. No, because the p-value for this test is equal to .1164
B. Yes, because the test value 1.257 is less than the critical value 1.782
C. No, because the test value 1.257 is greater than the critical value 1.115
D. Yes, because the test value 1.257 is less than the critical value 2.179

Explanation / Answer

Given n=13, xbar=473.46, s= 210.77 (based on the data)

The test hypothesis is
Ho:<=400
Ha:>400

The test statistic is

t=(xbar - )/(s/n)

=(473.46 - 400)/(210.77 /sqrt(13))

=1.257

Given =0.05, the critical value is |t(0.05, df=n-1=12)|=1.78 (check student t table)

The p-value is P(t > 1.26) = 0.1158 (check student t table)

Since t=1.257<1.78, we do not reject Ho.

Answer:A. No, because the p-value for this test is equal to .1164

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