Question

A genetics engineer was attempting to cross a tiger and a cheetah. She crossed 150 tigers and cheetahs. Based on prior research she expected that 5% of the animals would have no stripes or spots, 5% would have 3 spots only, 45% a phenotypic outcome of stripes only: and 45% would have both stripes and spots. When the cross was performed and she counted the individual cubs she found 25 without stripes, 50 with stripes only, 40 with 3 spots only and 35 with both. Conduct a hypothesis test.    

a.         State the null and research hypothesis

b.        Set the level of risk

c.         Select the appropriate test

d.        Compute the obtained value.

e.         Find the critical value

f.         Compare the obtained value and the critical value.

g.         State your decision.

h.        Write the result

Answer 1

Here we need to use chi square goodness of fit test.

(a)

Hypotheses are:

H0: The data follows the distribution of stripes and dots on cubs as expected.

Ha: The data does not follow the distribution of stripes and dots on cubs as expected.

(b)

The level of risk is

(c)

Chi square goodness of fit test

(d)

Following table shows the calculations:

	O	p	E=p*150	(O-E)^2/E
Without stripes	25	0.05	7.5	40.83333333
stripes only	50	0.45	67.5	4.537037037
3 spots only	40	0.05	7.5	140.8333333
both	35	0.45	67.5	15.64814815
Total	150		150	201.8518519

So test statistics is

(e)

Degree of freedom: df=4-1 = 3

The critical value is: 7.814

f)

g)

reject H0

h)

We cannot conclude that the data follows the distribution of stripes and dots on cubs as expected.