A TV manufacturer claims that the life span of its regular TV sets is 12 years with a standard
deviation of 1.2 years. Using a random sample of their 20 TV sets, the average life span is found
to be 11.2 years. Test the hypothesis that the T sets’ life span of 12 years as claimed by the
manufacturer is true at 0.05 level.
The following null and alternative hypotheses need to be tested:
This corresponds to a two-tailed test, for which a z-test for one mean, with known population standard deviation will be used.
Based on the information provided, the significance level is
and the critical value for a two-tailed test is
The rejection region for this two-tailed test is
The z-statistic is computed as follows:
Since it is observed that it is then concluded that the null hypothesis is rejected.
Using the P-value approach:
The p-value is and since it is concluded that the null hypothesis is rejected.
Therefore, there is enough evidence to claim that the population mean
is different than 12, at the significance level.
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