It is two-tailed test.
Let's test the hypothesis on 5% significance level.
Computing test statistic:
Since the sample is small (n=6 is less than 30), we use t-test with 6–1=5 degrees of freedom.
According to t-table with 5% significance level and 5 df the critical value is
Since test-statistic does not fall into the critical region,
–2.571 < –0.364 < 2.571, we accept the null hypothesis.
At the 5% significance level the data provide sufficient evidence to conclude that the population mean is 1500. We are 95% confident to conclude that the manufacturer’s claim was correct and the light bulbs have an average life time of 1500 hours.
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