What statistical test is needed for and what would the mathematical expression a

Question

What statistical test is needed for and what would the mathematical expression and hypothesis be for:

1. An experiement on the growth of monitor lizard chondrocytes in tissue culture that was tested under different temperatures with the goal of predicting thier growth rate at all temperatues within the range tested.

2. A number of environmental measurements were done at various corn fields. The researchers are interested in determining which soil types, groundwater level, slope, proximity to windbreaks, and irrigation systems occur when yields are high.

Explanation / Answer

Question 1

For this scenario, we need to use the one way analysis of variance or Single factor ANOVA F test for testing the hypothesis whether there is a statistically significant difference exists between the average growth of monitor lizard chondrocytes in tissue culture at different temperatures. If we take readings for more than two different temperatures, we will use one way ANOVA and then finding F test statistic we will make decision about null hypothesis. Null and alternative hypothesis for this test is given as below:

H0: µ1 = µ2 = …..= µi versus Ha: At least two µi’s are different.

Question 2

For this scenario, we need to use the two way analysis of variance F test. There are more than two factors and each factor have two levels. Factors are given as soil types, groundwater level, slope, proximity to windbreaks, and irrigation systems. Two levels are given as yields are high and yields are low. The null and alternative hypothesis for this test is given as below:

H0: µ11 = µ12 = …..= µij versus Ha: At least two µij’s are different, where i = 1, 2, 3, 4, 5, and j = 1, 2

i represents 5 factors, j represents 2 levels

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