Question

or questions 24-25 answer all the following questions: a)State the Null and Alternate H potheses b) Which is the claim? c) Will you use a z-test, t-test or chi- square test? What is the critical v d) Describe the reject repion as i e) Find the sample statistic 1) Do you reject the claim? Write out your decision in at least one sentence eft tailed, right tailed or two-tailed. 24. The Healthy Food Company makes an Oatmeal and Almond cereal. It has three ompetitors who make a similar product. The company wants to investigate if the percentage of people who consume Oatmeal and Almond cereal is the same for each of the four brands. Let A represent the Healthy Food Company's and B, and D represent the 3 competitors. A sample of 1000 person who consume Oatmeal and Almond cereal and they were asked which brand they consumed. The results are provided in the table below Cereal Brand AB adand Consumption 212 284 254 250 Does the sample provided on this table provide enough evidence to reject the null hypothesis that the percentage of people who consume Oatmeal and Almond cereal is th ame for all four brands? Use a significance level of 5% 25·The Smokey Bear Rangers station came out with a report in 201 0 that said 61% Of forest fires arestarted 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 recorded581 Assuming the Smokey Bear Rangers percentage test at the 2.5% sgntcance level whether the current distribution of the causes of forest fires is different from the 2010 report + 25 138 256 s are correct for the year 2010

Answer 1

24. Expected proportion for each Brand = 1/4 = 0.25

The following table is obtained.

Categories	Observed	Expected	(fo-fe)2/fe
A	212	1000*0.25=250	(212-250)2/250 = 5.776
B	284	1000*0.25=250	(284-250)2/250 = 4.624
C	254	1000*0.25=250	(254-250)2/250 = 0.064
D	250	1000*0.25=250	(250-250)2/250 = 0
Sum =	1000	1000	10.464

a) Null and Alternative Hypotheses:

H0 ​: The percentage of people who consume Oatmeal and Almond is the same for all four brands.

H1 ​: The percentage of people who consume Oatmeal and Almond is the not same for all four brands.

b) Claim: H0 ​: The percentage of people who consume Oatmeal and Almond is the same for all four brands.

c) We will use Chi-Square test for Goodness of Fit.

df = 4-1 = 3

Critical value:  
χ²_α = CHISQ.INV.RT(0.05, 3) = 7.815

d) Rejection Region

Reject Ho if χ² >7.815.

it is right tailed.

e) Test Statistics

(Oİ-E)2 = 5.776 +4.624 +0.064 +0 = 10.464 X2 = Ei i= 1

f) Since χ² >7.815, we reject the null hypothesis.

yes, we reject the claim.

There is not enough evidence to support the claim that the percentage of people who consume Oatmeal and Almond is the same for all four brands at 0.05 significance level.