Question

3) A stock market analyst wants to determine if the recent Hotel C upgrade to 4 starts has changed the distribution of shares of the hotel market. The current market share for the existing 3 hotels is shown in table below. The analyst collects data from a random sample of 200 investors. The table below shows the observed investors’ share holdings (f_i ). When using this random sample the analyst needs to be 90% confident of test results. The hypothesis to be tested follows:

H₀ : P_a =0.25; P_b =0.45; P_c =0.30 ; market shares have remained same

H_a : P_a ≠0.25; P_b ≠0.45; P_c ≠0.30 ; market shares have changed

Hotel Name	Current Market Share	Observ. Freq fi
A	0.25	50
B	0.45	95
C	0.30	55
Totals		200

1. Compute the test statistic

B. Has the recent upgrade of Hotel C to 5 stars changed the hotel market composition? Why?

Answer 1

( a )

The following table is obtained:

Categories	Observed	Expected	(fo-fe)2/fe
Category 1	50	200*0.25=50	(50-50)2/50 = 0
Category 2	95	200*0.45=90	(95-90)2/90 = 0.278
Category 3	55	200*0.30=60	(55-60)2/60 = 0.417
Sum =	200	200	0.694

from the above calculated table

Test Statistics

Rejection Region

Based on the information provided, the significance level is α = 0.10, the number of degrees of freedom is df = 3−1 = 2, so then the rejection region for this test is R = { χ2:χ2 > 4.605}.

Decision about the null hypothesis

Since it is observed that χ2 = 0.694 ≤ χc2 ​= 4.605, it is then concluded that the null hypothesis is not rejected.

( b )

No the recent upgrade of Hotel C to 5 stars does not  changed the hotel market composition . Because the null hypothesis is not rejected. so market shares have remained same and also Hotel C.