Respuesta :
Answer:
The mean life is actually less than the 100 hours the company claims.
Step-by-step explanation:
In this case we need to test whether the mean life is actually less than the 100 hours the company claims.
The information provided is:
[tex]n=20\\\bar x=98.5\\s=0.777[/tex]
The hypothesis for the test can be defined as follows:
H₀: The mean life 100 hours, i.e. μ = 100.
Hₐ: The mean life is actually less than the 100 hours, i.e. μ < 100.
Assume the significance level as 5%.
As the population standard deviation is not known we will use a t-test for single mean.
Compute the test statistic value as follows:
[tex]t=\frac{\bar x-\mu}{s/\sqrt{n}}=\frac{98.5-100}{0.777}=-1.93[/tex]
Compute the p-value of the test as follows:
[tex]p-value=P(t_{n-1}<-1.93)=P(t_{19}<-1.93)=0.034[/tex]
*Use a t-table.
Thus, the p-value of the test is 0.034.
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.
p-value = 0.034 < α = 0.05
The null hypothesis will be rejected at 5% level of significance.
Thus, concluding that the mean life is actually less than the 100 hours the company claims.
