Question

For questions 24 – 25 answer all the following questions:

a)State the Null and Alternate Hypotheses

b) Which is the claim?

c) Will you use a z-test, t-test or chi-square test? What is the critical value?

d) Describe the reject region as left tailed, right tailed or two-tailed.

e) Find the sample statistic.

f) Do you reject the claim? Write out your decision in at least one sentence.

25. The Smokey Bear Rangers station came out with a report in 2010 that said 61% of forest fires are started by accident, 24% by lighting, 13% by arson and 2% of the causes are unknown.   A 2017 study of 1000 randomly selected forest fire fighting companies was taken and the results of this sampling is recorded below.

Cause of Forest Fire	Accident	Lighting	Arson	Unknown
Number recorded	581	256	138	25

Assuming the Smokey Bear Rangers percentages are correct for the year 2010 test at the 2.5% significance level whether the current distribution of the causes of forest fires is different from the 2010 report.

Answer 1

Ans:

a)

H0:Current distribution of the causes of forest fires is same as the 2010 report.

Ha:Current distribution of the causes of forest fires is different from the 2010 report.

b)H0 is claim

c)alpha=0.025

df=4-1=3

critical chi square value=CHIINV(0.025,3)=9.348

Reject H0 if chi square>9.348

d)Right tailed

e)

Cause	Observed(fo)	percentage	Expected	(fo-fe)^2/fe
Accident	581	61%	610	1.379
Lighting	256	24%	240	1.067
Arson	138	13%	130	0.492
unknown	25	2%	20	1.250
Total	1000	100%	1000	4.188

Test statistic:

Chi square=4.188

f)Do not reject H0.

There is not sufficient evidence to conclude that the current distribution of the causes of forest fires is different from the 2010 report.