The data in the table below are measurements of hemoglobin (grams per 100 ml) in

Question

The data in the table below are measurements of hemoglobin (grams per 100 ml) in the blood of brown trout. The trout were placed at random in four different troughs. The fish food added to the troughs contained, respectively 0, 5,10 and 15 grams of sulfamerazine per 100 pounds of fish (coded 1,3, 4). The measurements were made on ten randomly selected fish from each trough after 35 days. Write out a suitable statistical (theoretical) model for this experiment. Write out the hypotheses tested. Conduct the appropriate statistical analysis on the data to draw conclusions regarding the mean level of hemoglobin as a function of sulfamerazine. Calculate a 95% upper confidence limit for the error variance

Explanation / Answer

There are 4 groups namely 1,2,3 and 4.

Here we have to test the hypothesis that,

H0 : mu1 = mu2 = mu3 = mu4 Vs H1 : Atleast one of the means is not equal.

where mu1 is population mean for code 1.

mu2 is population mean for code 2.

mu3 is population mean for code 3.

mu4 is population mean for code 4.

Assume alpha = 5% = 0.05

This we can done by usin ANOVA.

We can do hypothesis testing for ANOVA using EXCEL.

Steps are,

Data --> Data Analysis --> Anova : Single Factor --> ok --> Input Range : select all range of observations --> Grouped by : Columns --> alpha : 0.05 --> Output Range : select any empty cell --> ok

Output is,

Calculated F = 5.6955 and F crit = 2.866

Also P-value = 0.003

P-value < alpha

Reject H0 at 5% level of significance.

Conclusion : At least one of the mean is different.

Anova: Single Factor SUMMARY Groups Count Sum Average Variance 1 10 72 7.2 1.037778 2 10 93.3 9.33 2.946778 3 10 90.3 9.03 1.289 4 10 86.9 8.69 1.001 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 26.80275 3 8.93425 5.695543 0.002685 2.866266 Within Groups 56.471 36 1.568639 Total 83.27375 39

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