Question

Toyota Camry, Honda Accord and Ford F-150 are the top 3 best-selling passenger cars in the U.S for the last 5 years. Data for 2017 is shown in the table below. Your interest is to determine whether the shares in the passenger car market have changed in 2018. Use an alpha of 0.01 on your test.

	2017 MARKET SHARE	OBSERVED IN 2018
TOYOTA CAMRY	0.40	70
HONDA ACCORD	0.20	70
FORD F-150	0.40	60
TOTAL	100%	200

4.E) What is your decision after performing the test? (Accept or Reject)4.D) What is the critical value for the given alpha?
4.C) What is the value of degrees of freedom?
4.B) What is the value of the test statistic you calculated for this problem?4.A) What is the expected value for each category?

4.F) What is your conclusion after performing the test? Be specific and relate to the problem.

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: The shares in the passenger car market has not changed in 2018.

Alternative hypothesis: The shares in the passenger car market have changed in 2018.

Formulate an analysis plan. For this analysis, the significance level is 0.01. Using sample data, we will conduct a chi-square goodness of fit test of the null hypothesis.

Analyze sample data. Applying the chi-square goodness of fit test to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the P-value.

C)

DF = k - 1 = 3 - 1
D.F = 2
A)

(E_i) = n * p_i

	Observed in 2018	Expected	[(Or,c - Er,c)2/ Er,c]
Toyoto Camry	70	80.00	1.25
Honda Accord	70	40.00	22.5
Ford F - 150	60	80.00	5
Total	200	200	28.75

B)

X² = 28.75

D) X²_Critical = 9.221

E) Rejection region is X² > 9.221.

where DF is the degrees of freedom, k is the number of levels of the categorical variable, n is the number of observations in the sample, E_i is the expected frequency count for level i, O_i is the observed frequency count for level i, and X² is the chi-square test statistic.

Interpret results. Since the X² -value (9.221) lies in the rejection region, hence we have to reject the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that the shares in the passenger car market have changed in 2018.