Question

# 11. It is known that white sharks grow to a mean length of 20.2 feet. A...

11. It is known that white sharks grow to a mean length of 20.2 feet. A marine biologist claims that the great white sharks off the coast of Bermuda grow much longer. Fourteen great white sharks are captured, measured, and released off of Bermuda’s coast. The mean length is 21.92 feet and the standard deviation is 2.7 feet. Does the data provide sufficient evidence at the .05 level of significance to support the biologist’s claim?

Solution :

= 20.2

=21.92

s =2.7

n = 14

This is theright tailed test .

The null and alternative hypothesis is ,

H0 :    = 20.2

Ha : > 20.2

Test statistic = z

= ( - ) / s / n

= (21.92 - 20.2) / 2.7/ 14

= 2.384

Test statistic = t =2.384

P-value =0.0165

= 0.05

P-value <

0.0165 < 0.05

Reject the null hypothesis .

There is sufficient evidence to claim that the population mean μ is greater than 20.2 , at the 0.05 significance level.

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