The makers of Fizpop know that, in the past, 40% of their sales were from people

Question

The makers of Fizpop know that, in the past, 40% of their sales were from people under 30 years old, 45% of their sales were from people who are between 30 and 50 years old, and 15% of their sales were from people who are over 50 years old. A sample of 300 customers was taken to see if the market shares had changed. In the sample, 100 of the people were under 30 years old, 150 people were between 30 and 50 years old, and 50 people were over 50 years old. State the null and alternative hypotheses to be tested. Run a goodness of fit test at the 10% level of significance. Show all your work by hand using a test statistic/ critical value approach. What is your conclusion?

Explanation / Answer

null hypotheis: p1=0.4 ; p2=0.45 ; p3=0.15

alternate hypothesis: at least two of them is not as per above

from above given data below is the goodness of fit data

here chi stat =5.56

degree if freedom =2

for 2 degree of freedom and above chi stat p value=0.0622

as p vlaue is less then 0.1 level; we can reject null hypothesis.

also critical value of chi stat at 2 degree of freedom =4.605

as chi stat is higher then chi critical we can reject null hypothesis

observed Expected Chi square Attempted units P O E=total*p =(O-E)^2/E <30 years 0.4 100 120 3.33 30-50 0.45 150 135 1.67 >50 0.15 50 45 0.56 300 300 5.56

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