Question

Years	2007	2008	2009	2010	2011	2012	2013	2014	2015	2016	2017
Retail Sales	5.2%	0.3%	-3.3%	3.0%	4.9%	3.9%	3.1%	4.2%	3.8%	3.9%	3.6%
e-commerce Sales	19%	4.1%	2.8%	17.1%	17.5%	14.9%	13.0%	14.6%	14.7%	14.0%	16.0%

Does Retail Stores Growth Reduced by E-commerce Growth?

Null Hypothesis: H_o: Retail stores growth doesn’t reduce by E-commerce growth.

Alternative Hypothesis: H_a: Retail stores growth does reduce by E-commerce growth

Do the chi-square test for goodness of fit. with the level of significance is 0.05

Answer 1

Solution:-

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

Null hypothesis: Retail stores growth doesn’t reduce by E-commerce growth.

Alternative hypothesis: Retail stores growth does reduce by E-commerce growth.

Formulate an analysis plan. For this analysis, the significance level is 0.05. 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.

DF = k - 1 = 11 - 1
D.F = 10
(E_i) = n * p_i


X² = 95.58

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.

The P-value is the probability that a chi-square statistic having 11 degrees of freedom is more extreme than 95.58.

We use the Chi-Square Distribution Calculator to find P(X² > 95.58) = less than 0.0001.

Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we have to reject the null hypothesis.

From the above test we can conclude that Retail stores growth does reduce by E-commerce growth.