Respuesta :
Answer:
The p-value of the test is 0.0043 < 0.01, which means that it can be concluded that the average differs from the population average.
Step-by-step explanation:
The average amount of time a person exercises daily is 22.7 minutes in a population. Test if the average differs from the population average.
At the null hypothesis, we test if it does not differ, that is, the mean is of 22.7 minutes. So
[tex]H_0: \mu = 22.7[/tex]
At the alternate hypothesis, we test if it does differ, that is, if the mean is different of 22.7 minutes. So
[tex]H_1: \mu \neq 22.7[/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.
22.7 is tested at the null hypothesis:
This means that [tex]\mu = 22.7[/tex]
A random sample of 20 people showed an average of 29.8 minutes in time with a standard deviation of 9.8 minutes.
This means that [tex]n = 20, X = 29.8, s = 9.8[/tex]
Value of the test statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{29.8 - 22.7}{\frac{9.8}{\sqrt{20}}}[/tex]
[tex]t = 3.24[/tex]
P-value of the test:
Using the t-distribution, testing if the mean is different, so a two-tailed test with t = 3.24 and 20 - 1 = 19 degrees of freedom.
Using a t-distribution calculator, the p-value of the test is of 0.0043.
The p-value of the test is 0.0043 < 0.01, which means that it can be concluded that the average differs from the population average.
