Respuesta :
Answer:
a)
[tex]H_0:\mu=2.4\\\\H_a:\mu>2.4[/tex]
b) t=1.172
c) The null hypothesis failed to be rejected.
There is no enough evidence to claim that the mean tornado length is greater than 2.4 miles.
Step-by-step explanation:
The question is incomplete:
The sample mean is 2.74 and the sample standard error is 0.29.
We have to test the claim that the mean tornado length is greater than 2.4 miles.
The appropiate null and alternative hypothesis are:
[tex]H_0:\mu=2.4\\\\H_a:\mu>2.4[/tex]
As the population standard deviation is not known, the sample standard deviation is used as an estimation. The statistic is T-student instead of the z-value.
[tex]t=\frac{M-\mu}{s/\sqrt{n}}=\frac{2.74-2.4}{0.29} =\frac{0.34}{0.29} =1.172[/tex]
The degrees of freedom are
[tex]df=n-1=400-1=399[/tex]
The P-value for this t-statistic is
[tex]P(t>1.172)=0.12[/tex]
At a significance level of 0.05, the P-value is greater, so the effect is not significant and the null hypothesis failed to be rejected.
There is no enough evidence to claim that the mean tornado length is greater than 2.4 miles.
