Respuesta :
Using the z-distribution, as we have the standard deviation for the population, it is found that the correct decision is given by:
Reject the null hypothesis. There is enough evidence to oppose the company's claim.
What are the hypothesis tested?
At the null hypothesis, it is tested if the mean is of 2.7 years, that is:
[tex]H_0: \mu = 2.7[/tex]
At the alternative hypothesis, it is tested if the mean is different of 2.7 years, hence:
[tex]H_1: \mu \neq 2.7[/tex]
What is the test statistic?
The test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
The parameters are:
- [tex]\overline{x}[/tex] is the sample mean.
- [tex]\mu[/tex] is the value tested at the null hypothesis.
- [tex]\sigma[/tex] is the standard deviation of the sample.
- n is the sample size.
In this problem, the values of the parameters are given by:
[tex]\overline{x} = 3.1, \mu = 2.7, \sigma = 0.85, n = 25[/tex]
Hence, the value of the test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{3.1 - 2.7}{\frac{0.85}{\sqrt{25}}}[/tex]
[tex]z = 2.35[/tex]
What is the decision?
Considering a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.05, the critical value is of [tex]|z^{\ast}| = 1.96[/tex].
Since the absolute value of the test statistic is greater than the critical value, the correct decision is:
Reject the null hypothesis. There is enough evidence to oppose the company's claim.
More can be learned about the z-distribution at https://brainly.com/question/16313918
