Question

A data set includes data from 400 random tornadoes. The display from technology available below results from using the tornado lengths​ (miles) to test the claim that the mean tornado length is greater than 2.4 miles. Use a 0.05 significance level. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim. LOADING... Click the icon to view the display from technology. What are the null and alternative​ hypotheses? A. Upper H 0​: muequals2.4 miles Upper H 1​: muless than2.4 miles B. Upper H 0​: muless than2.4 miles Upper H 1​: muequals2.4 miles Your answer is not correct.C. Upper H 0​: muequals2.4 miles Upper H 1​: munot equals2.4 miles D. Upper H 0​: muequals2.4 miles Upper H 1​: mugreater than2.4 miles This is the correct answer. Identify the test statistic. nothing ​(Round to two decimal places as​ needed.)

Answer 1

Answer:

a)

$H_0:\mu=2.4\\\\H_a:\mu>2.4$

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:

$H_0:\mu=2.4\\\\H_a:\mu>2.4$

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.

$t=\frac{M-\mu}{s/\sqrt{n}}=\frac{2.74-2.4}{0.29} =\frac{0.34}{0.29} =1.172$

The degrees of freedom are

$df=n-1=400-1=399$

The P-value for this t-statistic is

$P(t>1.172)=0.12$

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.