Exercise Quiz 12

Four tasters evaluated the sweetness of five products on a scale from 0 to 10 with the following results:

Product	taster 1	taster 2	taster 3	taster 4
product 1	6	8	10	7
product 2	3	5	8	4
product 3	10	9	9	8
product 4	7	6	6	6
product 5	8	8	10	7

The critical value for the usual test of the hypothesis that there is no difference between the five products when data is assumed to be normal and $\alpha = 5\%$ is:

$F(4,15)_{0.05}=3.06$

$F(4,12)_{0.05}=3.26$

$F(5,12)_{0.05}=3.11$

$F(3,12)_{0.05}=3.49$

$F(5,15)_{0.05}=2.90$

The so-called cell-number in a sample of milk expresses the degree of inflammation of the udder (mastitis). The logarithm of the cell-number was observed in samples of milk taken from 166 sheep (one sample per sheep) from a total of 3 herds. The average cell-number in all 166 sheep was 4.896. The following table shows some basic numbers for the calculations.

Herd	Number of sheep	Mean	Standard deviation
Herd 1	39	4.823	1.654
Herd 2	67	5.293	1.706
Herd 3	60	4.499	1.746

The usual test statistic for testing if there is a difference in the level of cell-number in the three herds is:

$\frac{\left[39\cdot (4.823-4.896)^2+67\cdot (5.293-4.896)^2+60\cdot (4.499-4.896)^2\right]} {\left[39\cdot 1.654^2+67 \cdot 1.706^2+60\cdot 1.746^2\right]}$

$\frac{\left[38\cdot 4.823^2+66\cdot 5.293^2+59\cdot 4.499^2 \right]/2} {\left[38 \cdot 1.654^2+66\cdot 1.706^2+59\cdot 1.746^2\right]}$

$\frac{\left[39\cdot (4.823-4.896)^2+67\cdot (5.293-4.896)^2+60\cdot (4.499-4.896)^2\right]/3} {\left[38\cdot 1.654+66\cdot 1.706+59\cdot 1.746\right]/166}$

$\frac{\left[39\cdot (4.823-4.896)^2+67\cdot (5.293-4.896)^2+60\cdot (4.499-4.896)^2\right]/2} {\left[38\cdot 1.654+66\cdot 1.706+59\cdot 1.746\right]/163}$

$\frac{\left[39\cdot (4.823-4.896)^2+67\cdot (5.293-4.896)^2+60\cdot (4.499-4.896)^2\right]/2} {\left[38\cdot 1.654^2+66\cdot 1.706^2+59\cdot 1.746^2\right]/163}$

02323 · Exercise Quiz 12

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