Respuesta :
Answer:
Since the pvalue of the test is 0 < 0.01, we reject the null hypothesis and accept the alternate hypothesis that the true mean score for all sober subjects is different of 35.
Step-by-step explanation:
Test the claim that the true mean score for all sober subjects is equal to 35.0.
This means that the null hypothesis is:
[tex]H_{0}: \mu = 35[/tex]
And the alternate hypothesis is:
[tex]H_{a}: \mu \neq 35[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
35 is tested at the null hypothesis:
This means that [tex]\mu = 35[/tex]
Sample of 20, mean score of 41.0 with a standard deviation of 3.7.
This means that [tex]n = 20, X = 41, \sigma = 3.7[/tex]
Value of test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{41 - 35}{\frac{3.7}{\sqrt{20}}}[/tex]
[tex]z = 7.25[/tex]
Pvalue of the test:
The pvalue of the test is the probability that differs from the mean by at least 41 - 35 = 6, which is the probability that |z| < 7.25.
z = -7.25 has a pvalue of 0
2*0 = 0
Since the pvalue of the test is 0 < 0.01, we reject the null hypothesis and accept the alternate hypothesis that the true mean score for all sober subjects is different of 35.
