Question

5. Mongolian gerbils are thought to be equally likely to be brown, white, or black in color. A random sample showed the following frequencies: White Black Brown 40 59 42 count (a) State the mull hypothesis (b) State the alternative hypothesis. (c) Calculate the test-statistic. (d) Estimate the p-value. (e) Using a 0.1, do we reject or fail to reject the null? (f) State your conclusion in terms of the problem (g) What category differed the most from what we expected if the mull hypothesis was true?

Answer 1

(a)

H0: Null Hypothesis: Mongolian Gerbils are equally likely in color (Claim)

(b)

HA: Al$\chi ^{2}$ternative Hypothesis: Mongolian Gerbils are not equally likely in color

(c)

The Test Statistic $\chi ^{2}$ is got as follows:

Color	Observed (O)	Expected (E)	(O - E)2/E
Black	40	47	1.0426
Brown	59	47	3.0638
White	42	47	0.5319
Total = $\chi ^{2}$ =			4.6383

(d)

By Technology, p - value = 0.0984

(e)

Since p - value is less than $\alpha$ = 0.10, the difference is significant. Reject null hypothesis.

(f)

The data do not support the claim that Mongolian Gerbils are equally likely in color.

(g)

Brown differed the most.