2. A light-bulb manufacturer regularly advertises that his bulbs last 900 hours
with a standard deviation of 75 hours. A random sample is chosen before each
campaign to make sure that the claim is correct. If one such sample of 20 bulbs
show a mean of 925 hours, can the advertising claim be considered an
underestimate at the 0.05 level of significance?
The following null and alternative hypotheses need to be tested:
This corresponds to a right-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 right-tailed test is
The rejection region for thisright-tailed test is
The z-statistic is computed as follows:
Since it is observed that it is then concluded that the null hypothesis is not rejected.
Using the P-value approach:
The p-value is and since it is concluded that the null hypothesis is not rejected.
Therefore, there is not enough evidence to claim that the population mean
is greater than 900, at the significance level.
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