Chapter 11.1, Problem 15E

a)

To determine

To perform chi-square goodness of fit test.

Answer to Problem 15E

There is not sufficient evidence to reject the claim of Mendel’s belief.

Explanation of Solution

Given:

Observed count	Frequency
423	0.75
133	0.25

Calculation:

The null and alternative hypotheses:

  $H_0:p_1=\frac{3}{3+1}=\frac{3}{4}=0.75,p_2=1-0.75=0.25$

  $H_a:Atleastoneofthe{p}_i’sisincorrect.$

Using excel,

Observed	expected	O - E	(O - E)² / E	% of chisq
423	417.000	6.000	0.086	25.00
133	139.000	-6.000	0.259	75.00
Total=556	556.000	0.000	0.345	100.00
.35	chi-square
1	Df
.5568	p-value

Decision: P-value > 0.05, fail to reject H0.

Conclusion: There is not sufficient evidence to reject the claim of Mendel’s belief.

b)

To determine

To compare z test statistic and chi-square goodness of fit test

Answer to Problem 15E

There is not sufficient evidence to reject the claim of Mendel’s belief.

Explanation of Solution

Given:

Observed count	Frequency
423	0.75
133	0.25

Calculation:

Using chi-square test,

.35	chi-square
1	Df
.5568	p-value

Using z test,

Z = 0.588

P-value = 0.2784

Decision: P-value > 0.05, fail to reject H0.

From both results, we can conclude thatthere is not sufficient evidence to reject the claim of Mendel’s belief.