Respuesta :
Answer:
The test statistic is t = 2.5.
The p-value of the test is of 0.007 < 0.05, which means that the evidence supports the manufacturer's claim at the .05 significance level.
Step-by-step explanation:
Mean life of 600 hours. Test if it is more.
At the null hypothesis, we test if the mean is of 600 hours, that is:
[tex]H_0: \mu = 600[/tex]
At the alternative hypothesis, we test if the mean is of more than 600 hours, that is:
[tex]H_1: \mu > 600[/tex]
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.
600 is tested at the null hypothesis:
This means that [tex]\mu = 600[/tex]
Suppose 100 bulbs were tested and found to have a mean of 625 hours with a standard deviation of 100.
This means that [tex]n = 100, X = 625, s = 100[/tex].
Value of the test-statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{625 - 600}{\frac{100}{\sqrt{100}}}[/tex]
[tex]t = 2.5[/tex]
The test statistic is t = 2.5.
P-value of the test and decision:
The p-value of the test is the probability of finding a sample mean above 625 hours, which is a right-tailed test, with t = 2.5 and 100 - 1 = 99 degrees of freedom.
Using a t-distribution calculator, this p-value is of 0.007.
The p-value of the test is of 0.007 < 0.05, which means that the evidence supports the manufacturer's claim at the .05 significance level.
