Question

The diameter (in millimeters) for 34 sand dollar (Dendraster excentricus) shells (tests) collected from beaches in Morro Bay was measured. A stem-and-leaf plot constructed from this sample data appears below.

2 | 5 6 9

3 | 0 1 1 2 3 4 4 5 7

4 | 2 3 5 5 6 8 9 9

5 | 1 4 4 6 7 7

6 | 0 2 2 4 5

7 | 3 6 7

Use this data with α = 5% to test the validity of the hypothesis that, for beaches in Morro Bay, the mean sand dollar shell diameter is 45 mm.

Answer 1

For the given sample

25,26,29,30,31,31,32,33,34,34,35,37,
42,43,45,45,46,48,49,49,
51,54,54,56,57,57,60,62,62,64,65,73,76,77

sample mean=xbar=sum of values/total=1612/34= 47.41176

sample standard deviation=s= 14.71984

sample size=n=34

Conduct t test for mean

Ho:

Ha:

alpha=0.05

Test statistic,

t=xbar-mu/s/sqrt(n)

=(47.41176-45)/(14.71984/sqrt(34))

t=0.9553675

df=n-1=34-1=33

p value for two tail t test in excel

=T.DIST.2T(0.9553675,33)

=0.346338539

p=0.3463

p>0.05

Fail to reject Ho

Accept Ho

Conclusion:
There is suffcient statitstical evdience at 5% level of significance to conclude that the mean sand dollar shell diameter is 45 mm.