Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
Sagot :
Using the t-distribution, as we have the standard deviation for the sample, it is found that since the absolute value of the test statistic is greater than the critical value for the two-tailed test, there is enough evidence to conclude that the sample does not come from a population whose mean is 1,600 hours.
What are the hypothesis tested?
At the null hypothesis, it is tested if the mean is of 1600 hours, that is:
[tex]H_0: \mu = 1600[/tex]
At the alternative hypothesis, it is tested if the mean is different of 1600 hours, that is:
[tex]H_1: \mu \neq 1600[/tex]
What is the test statistic?
It is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\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.
- s is the standard deviation of the sample.
- n is the sample size.
In this problem, the values of the parameters are:
[tex]\overline{x} = 1500, \mu = 1600, s = 120, n = 100[/tex]
Hence, the value of the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{1500 - 1600}{\frac{120}{\sqrt{100}}}[/tex]
[tex]t = -8.33[/tex]
What is the decision rule?
Considering a two-tailed test, as we are testing if the mean is different of a value, with 100 - 1 = 99 df and a significance level of 0.01, the critical value is of [tex]t^{\ast} = 1.66[/tex].
Since the absolute value of the test statistic is greater than the critical value for the two-tailed test, there is enough evidence to conclude that the sample does not come from a population whose mean is 1,600 hours.
More can be learned about the t-distribution at https://brainly.com/question/13873630
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.
