Question

A data set includes data from 500 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 2.6 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?

Hypothesis test? results:

mu?

?: Mean of variable
H0

? :
mu?equals=2.62.6

HA

? :
mu?greater than>2.62.6

Variable

Sample Mean

Std. Err.

DF

?T-Stat

?P-value

Length

3.236013.23601

0.2851850.285185

499499

2.2301662.230166

0.01310.0131

A. Upper H0?: mu ? < 2.6 miles Upper H 1?: mu ? equals = 2.6 miles

B. Upper H0?: mu ? equals = 2.6 miles Upper H1?: mu ? not equals ? 2.6 miles

C. Upper H0?: mu ? equals =2.6 miles Upper H1?: mu ? less than <2.6 miles

D. Upper H0?: mu ? equals = 2.6 2.6 miles Upper H 1 H1?: mu ? > 2.6 miles

Identify the test statistic. nothing ?(Round to two decimal places as? needed.)

Identify the? P-value. nothing ?(Round to three decimal places as? needed.) State the final conclusion that addresses the original claim.

? (Fail to reject, Reject) Upper H0. There is ?( sufficient, not sufficient) evidence to support the claim that the mean tornado length is greater than 2.6 miles

Answer 1

The null and alternative hypothesis are:

`H_0:\mu =2.6\\H_a:\mu >2.6`

There is sufficient evidence to support the claim that the mean tornado length is greater than 2.6 miles

Explanation:

Consider the provided information.

The claim that the mean tornado length is greater than 2.6 miles.

If there is no statistical significance in the test then it is know as the null which is denoted by
`H_0`, otherwise it is known as alternative hypothesis which denoted by
`H_a`.

Therefore, the required null and alternative hypothesis are:

`H_0:\mu =2.6\\H_a:\mu >2.6`

significance level α =0.05

From the given table the test statistic T=2.230166

P-value is 0.0131

0.0131<0.05

P value is less than the significance level, so reject the null hypothesis.

There is sufficient evidence to support the claim that the mean tornado length is greater than 2.6 miles