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 2.9 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.

Hypothesis test​ results:
	muμ ​: Mean of variable
	H0 ​ : muμequals=2.92.9
	HA ​ : muμgreater than>2.9

Variable	Sample Mean	Std. Err.	DF	​T-Stat	​P-value
	Length	3.516113.51611	0.2858940.285894	499499	2.1550292.155029	0.01580.0158

b) Identify the test statistic.

c) Identify the​ P-value.

Answer 1

= 2.9, = 3.516113, SE = 0.285894, n = 500, df = n - 1 = 499

(a) The Hypothesis:

H0: = 2.9

Ha: > 2.9

This is a right tailed Test.

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(b) The Test Statistic:

The test statistic is given by the equation:

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(c) The p value (right tailed) at t (2.1550292, 499) = 0.0158

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(d) The Conclusion: Since p value is < Alpha (0.05)

Reject H0. There is sufficient evidence to conclude that the mean toranado length is greater than 2.9 miles.

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The p Value:    The p value (Right Tail) for t = , for degrees of freedom (df) = n-1 = , is; p value =