For questions 24-25 answer all the following questions: a)State the Null and Alt

Question

For questions 24-25 answer all the following questions: a)State the Null and Alternate Hypotheses b) Which is the claim? c) W ill 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. Do you reject the claim? Write out your decision in at least one sentence. 24. The Healthy Food Company makes an competitors who make a similar product. The company wants to investigate if he 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 A Consumption 212284 254 250 Does the sample provided on this table provide enough evidence to reject the 5% null hypothesis that the percentage of people who consume Oatmeal and Almond cereal is the same for all four brands? Use a significance level of 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.

Explanation / Answer

Q24.

observed frequncies are Oi

212 284 254 250   

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expected frequencies are Ei

=1000/4 = 250   

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and claiming hypothesis is

null, Ho: no association exists b/w them OR observations are independent

alternative, H1: exists association b/w them OR observations are dependnet

level of significance, = 0.05

from standard normal table, chi square value at right tailed, ^2 /2 =5.9915

since our test is right tailed,reject Ho when ^2 o > 5.9915

we use test statistic ^2 o = (Oi-Ei)^2/Ei

from the table take sum of (Oi-Ei)^2/Ei, we get ^2 o = 10.464

critical value

the value of |^2 | at los 0.05 with d.f, n - 1 = 3 - 1 = 2 is 5.9915

we got | ^2| =10.464 & | ^2 | =5.9915

make decision

hence value of | ^2 o | > | ^2 | and here we reject Ho

^2 p_value =0.0053

ANSWERS

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null, Ho: no association exists b/w them OR observations are independent

alternative, H1: exists association b/w them OR observations are dependnet

test statistic: 10.464

critical value: 5.9915

p-value:0.0053

decision: reject Ho

the percentage of people who consume oatmeal and almond cereal is diffrent among four groups

Observed (Oi ) Expected ( Ei) Oi-Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 212 250 -38 1444 5.776 284 250 34 1156 4.624 254 250 4 16 0.064 250 250 0 0 0

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