Question

Hypothesis Test: Show the 5 Steps. (2 marks) "Hot wheels" magazine published an article stating that car brands are purchased in equal numbers. To examine this claim, a sample of cars on a major highway was collected and the numbers of 5 major car brands was reported. The numbers are given in the table. Does this sample contradict the magazine's claim at the 0.10 level of significance. Honda Toyota Ford GM Hyundai 121105 98 ||92 102

Answer 1

H: Car brands purchased in an equal numbers H: Car brands purchased not an equal numbers Significance level: a = 0.10 The formula of chi square test statistic is, χ =Σ (0-E) E Here, O =Observed frequency. E = Expected frequency The expected frequency is, 121 +105 +98 +92 +102 518 E = 103.6 5 5 The below table describes the computation of chi square test statistic:

Car brands Honda Toyota Ford GM Hyundai O-E 17.400 observed 121 105 98 expected 103.6 103.6 (O-E2/E 2.922 0.019 0.303 1.299 0.025 1.400 -5.600 -11.600 -1.600 103.6 92 103.6 103.6 102 518 518 0.000 4.568 Therefore, the chi-square test statistic is Xo = 4.568 The degree of freedom is, df = k-1 = 5-1 = 4 P-value approach: p-value = P(x? > x) = CHIDIST (4.568,4) [From Excel fimction]

= 0.334560413 0.3346 Decision rule: Reject H , if psa otherwise do not reject H,- Since the p-value greater than the level of significance, so we fail to reject the null hypothesis at specified significance level. Conclusion: There is not sufficient evidence to warrant the rejection of the claim that car brands purchased in equal numbers No, the sample has not contradict the magazines claim