Past data suggests that the market shares of four firms (A, B, C, and D) are 30%
ID: 3049559 • Letter: P
Question
Past data suggests that the market shares of four firms (A, B, C, and D) are 30%, 25%, 15%, and 30% respectively. A random sample of 120 customers showed that 28 bought the product from A, 28 from B, 24 from C, and 40 from D.
We need to test whether this data provides evidence that the market shares have changed. The hypotheses are
H0: pA = 0.3, pB = 0.25, pC = 0.15, and pD = 0.3
H1: pA, pB, pC, pD are not as given above.
(here pA is the market share of A, i.e. the population proportion of customers who buy the product from A).
We need to test this at 5% level of significance.
What is the value of the appropriate test statistic? (Provide two decimal places)
Explanation / Answer
Ans:
Expected count=pi*120
From above table:
Calculated chi square score=4.80
df=4-1=3
p-value=chidist(4.80,3)=0.1870
As,p-value>0.05,we Fail to reject null hypothesis.
There is insufficient evidence to conclude that the market shares have changed.
Observed(O) pi Expected€ (O-E)^2/E A 28 0.3 36 1.778 B 28 0.25 30 0.133 C 24 0.15 18 2.000 D 40 0.3 36 0.444 Total= 120 1 120 4.36