Sprint - 17:13 campus.fsu.edu 80%-- 1. The genetic model that the agronomists we

Question

Sprint - 17:13 campus.fsu.edu 80%-- 1. The genetic model that the agronomists were considering predicted that the ratio of normal to shriveled progeny would be 3:1. They obtained 100 normal and 50 shriveled progeny. Conduct a chi- square goodness of fit test at the -05 level and a non-directional alternative to determine whether or not the data supports the hypothesized model. (You may use the following table to help keep track of your wovk) Normal Shriveled Formulas for #1 (0-E) z'=_.k is the number of categories, df = number of categories-1 2 of 2 2. A randomized experiment was conducted in which patients with coronary artery disease either had

Explanation / Answer

The observed values are Normal = 100 and shrivelled = 50. Total = 150.

Since the expected values are in the ratio 3:1,

The expected normal = 3*150/4 = 112.5 and

The expected for shrivelled = 1*150/4 = 37.5

The Hypothesis:

H0: There is no difference between the observed and expected values. (The data supports the hypothesized model).

Ha: There is a difference between observed and expected values. (The data does not support the hypothesized model).

The Test Statistic: The table below gives the calculation of 2.

2test = 5.55

The Critical Value:   The critical value at = 0.05 , degrees of freedom = k-1 = 1  

2critical = 3.841

The Decision Rule: If 2 test is > 2 critical, then Reject H0.

The Decision:    Since If 2 test (5.55) is > 2 critical (3.841), We Reject H0.

The Conclusion: There is sufficien evidence at the 95% significance level to conclude that there is a difference between observed and expected values. (The data does not support the hypothesized model).

Observed Expected Normal 100 112.5 Shrivelled 50 37.5 Total 150 150

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