Question

Last year, an entomologist was given a brand new indoor garden for his research. He decided to include in the indoor garden the following percentage of insects: 30% butterflies, 20% fireflies, 35% moths, and 15% of other types. A year has passed and he observed a random sample of 200 insects classified in the following table. He wants to conduct a test at 0.10 level of significance to see whether the proportions of insects differ significantly from the proportions that he started last year.

INSECTS IN THE INDOOR GARDEN
Butterflies	Fireflies	Moths	Other	Total
67	26	75	32	200

State the hypotheses.

H0: p1=.3, p2=.2, p3=.35, p4=.15, Ha: p1 not=.3, p2 not=.2, p3 not=.35, p4 not=.15

H0: p1=.3, p2=.2, p3=.35, p4=.15, Ha: At least one p is different from the hypothesized proportion.

H0: p1=.57, p2=.36, p3=.75, p4=.32, Ha: p1 not=.57, p2 not=.36, p3 not=.75, p4 not=.32

H0: p1=.285, p2=.18, p3=.375, p4=.16, Ha: At least one p is different from the hypothesized proportion.

Continue to consider Question #1.

Fill in the expected counts in the table. Round to whole numbers. Avoid any blank space. Partial credit is given.

Expected counts
Butterflies	Fireflies	Moths	Other

Continue to consider Question #1.

Find the value of test statistic.

Group of answer choices

0.31

0.82

8.73

6.21

Continue to consider Question #1.

Find the rejection region.

Group of answer choices

X² > 6.251

X² > 7.779

X² < 7.779

X² < 6.251

Continue to consider Question #1.

What’s your conclusion at 0.10 level of significance?

Group of answer choices

Reject H0. Sufficient evidence that the proportions of insects are the same as the proportions in the last year.

Do not reject H0. Sufficient evidence that the proportions of insects are the same as the proportions in the last year.

Do not reject H0. Insufficient evidence that the proportions of insects differ from the proportions in the last year.

Reject H0. Sufficient evidence that the proportions of insects differ from the proportions in the last year.

Answer 1

1)H0: p1=.3, p2=.2, p3=.35, p4=.15, Ha: At least one p is different from the hypothesized proportion.

since expected count =np

2)expeced count table"

Butterflies	Fireflies	Moths	Other
60	40	70	30

Applying test:

	relative	observed	Expected	residual	Chi square
category	frequency(p)	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
1	0.300	67.0	60.00	0.90	0.817
2	0.200	26.0	40.00	-2.21	4.900
3	0.350	75.0	70.00	0.60	0.357
4	0.150	32.0	30.00	0.37	0.133
total	1.000	200	200		6.2071
3)test statistic X2 =		6.21

4)rejection region

X² > 6.251

5)Do not reject H0. Insufficient evidence that the proportions of insects differ from the proportions in the last year.