Question

Researchers at Coastal Carolina University are interested in estimating the mean precaudal length of Atlantic Sharpnose sharks found in North Inlet. The distribution of the precaudal lengths can be assumed to be Normally distributed. A previous study in a similar inlet suggests that the average precaudal length of Atlantic Sharpnose sharks is 32 inches. Marine scientists catch and release 20 Atlantic Sharpnose sharks and find average precaudal length of 30.06 inches with standard deviation of 11.32 inches. Can we conclude that the mean length of the Atlantic Sharpnose is different from 32 inches?

Answer 1

Solution:

Here, we have to use one sample t test for population mean.

H₀: µ = 32 versus H_a: µ ≠ 32

This is a two tailed test.

We assume level of significance = α = 0.05

Xbar = 30.06

S = 11.32

n = 20

df = n – 1 = 19

Critical t value = -2.0930 and 2.0930

(by using t-table)

Test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

t = (30.06 – 32)/[11.32/sqrt(20)]

t = -0.7664

P-value = 0.4528

(by using t-table)

P-value > α = 0.05

So, we do not reject the null hypothesis

There is insufficient evidence to conclude that the mean length of the Atlantic Sharpnose is different from 32 inches.