Question

(9pt) A stock market analyst wants to determine if the recent introduction of the IPhone 8x has changed the distribution of shares in the cellphone market. The analyst collects data from a random sample of 300 cellphone customers. The table below shows the observed customers’ share of cellphones (fi ). When using this random sample, the analyst needs to be 95% confident of test results. The hypothesis to be tested follows: H0 : Plg =0.20; Pa =0.32; Ps =0.48 ; market shares have remained same Ha : Plg ≠0.20; Pa ≠0.32; Ps ≠0.48 ; market shares have changed Cellphone company Current Market Share Observ. fi Samsung 0.48 100 Apple 0.32 120 LG 0.20 80 Totals 300 a. (6pt) Compute the test statistic for a chi-squared test. b. (3pt) After the test, would you conclude that the introduction of the IPhone 8x has changed the market composition? Why?

Answer 1

The null hypothesis is :  H₀ : Plg =0.20; Pa =0.32; Ps =0.48

The alternative hypothesis is : H_a : Plg ≠0.20; Pa ≠0.32; Ps ≠0.48

Using Minitab software, (Stat -> Tables -> Chi Square Goodness of Fit Test), we get the following output :

The value of chi square statistic

and P-value = 0

Since P-value < 0.05, so we reject H₀ at 5% level of significance and we can conclude that there is sufficient evidence to support the claim that the introduction of the IPhone 8x has changed the market composition.