Question

Suppose there are 3 companies in the market for delivering food: Glovo, Wolt, and Tsrapi and you want to test if they all have the same/equal market shares. Based on a random sample of 300 people 82 reported using Glovo, 117 reported using Wolt and 101 reported using Tsrapi. Based on this evidence, and given 5% significance level, which statement below represents the test-statistic and the correct decision for this case?

Select one:

a. Test-statistic=6.14, we cannot reject the equality of market shares

b. Test-statistic=6.43, we cannot reject the equality of market shares

c. Test-statistic=6.14, we reject the equality of market shares

d. Test-statistic=6.43, we reject the equality of market shares

Answer 1

The given data is

	Observed frequency
Glovo	82
Wolt	117
Tsrapi	101
	300

We shall use Chi square test

The null and alternative hypothesis

H0: The distribution of market shares are equal for three companies

Ha : The distribution of market shares are not equal for three companies

Test statistic

where Oi : observed frequency

Ei : expected frequency

Under null hypothesis ,expected frequency for each cell is 100

Calculation of Chi square

	Observed frequency(Oi)	Expected frequency(Ei)	(Oi-Ei)^2/Ei
Glovo	82	100	3.24
Wolt	117	100	2.89
Tsrapi	101	100	0.01
sum			6.14

Thus

6.14

degrees of freedom = 3-1= 2

Critical value of chi square at 0.05 with 2 df

5.99 (from chi square table)

Since calculated value of > 5.99   

We reject H0

Answer is : Test statistic = 6.14 , we reject the equality of market shares .