The salinity of water samples from 4 separate sites in the Bimini Lagoon, Bahama

Question

The salinity of water samples from 4 separate sites in the Bimini Lagoon, Bahamas, was measured; the data are given below. (You can use statistical software, or better, calculate by hand or with a spreadsheet and check with software. Copying and pasting will avoid data entry errors.)

Site 1: 41.33 40.56 42.29 35.28 41.05 39.84 43.62
Site 2: 37.89 37.40 44.21 45.96 43.21 44.09 38.82 49.31 40.98 45.30
Site 3: 44.96 35.94 43.94 41.40 42.91 47.58 39.56 42.91
Site 4: 35.53 38.03 39.73 36.62 32.79 37.32 37.64 46.84 44.77 36.56 41.36 38.68

1.Calculate the test statistic.

2.Which interval in the table contains the p-value for the test? (Verify your answer by calculting the p-value with statistical software and using the appropriate table on the course site. You might have to improvise a little with the tables if your exact degrees of freedom aren't listed.)
p-value 0.001
0.001 < p-value 0.01
0.01 < p-value 0.05
0.05 < p-value 0.1
0.1 < p-value 0.25
p-value > 0.25

3. Would you reject the null hypothesis at = 0.05?

Explanation / Answer

From Excel

H0: There is no significant difference between means of four sites

H1: There is a significant difference between means of four sites

alpha:5%
Test statistic:

F cal=10.01

COnclsion:

Pvalue=0.0000457

P value<0.05 we reject the H0.

Hence claim is significant

Anova: Single Factor SUMMARY Groups Count Sum Average Variance site1 12 537.68 44.80667 24.73413 site2 12 472.69 39.39083 37.41979 site3 10 440.32 44.032 21.9832 site4 11 381.66 34.69636 11.57741 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 730.4299 3 243.4766 10.00941 4.47E-05 2.832747 Within Groups 997.316 41 24.32478 Total 1727.746 44

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