Moto owns a silk shop in Taipei City and want to expands color selection.
Before expanding colors, do the customers have a brand preference?
As an experiment, sales by brand were recorded on randomly selected days.
At the 0.10 significance level, can it be concluded that there is a difference in preference among the brands?
Cyan Pearl Onyx
724 776 829
709 640 961
798 822 824
845 812 950
720 673 761
800 893 867
6 What is the null hypothesis?
What is the alternative hypothesis?
7 The level of significance depends on the application. What is the level of significance (α) in this problem?
Perform single factor ANOVA using Data Analysis. Include the row 6 labels in the Input Range and check the Labels checkbox.
8 From the ANOVA output: What is the F test statistic?
What is the critical value of the F test statistic?
9 What is your decision in terms of H0, the significance level, the F test statistic, and the F test statistic critical value.
Analyzing Brand Preferences among Customers at a Silk Shop
Introduction
Moto, the owner of a silk shop in Taipei City, is contemplating expanding the color selection in the shop. Before making this decision, Moto wants to determine if customers have a brand preference among the existing options. By conducting a statistical analysis of sales by brand on randomly selected days, we can assess whether there is a significant difference in brand preference among customers.
Thesis Statement
The null hypothesis states that there is no difference in brand preference among customers for the Cyan, Pearl, and Onyx brands. Through a single-factor ANOVA test, we will evaluate the sales data to determine if there are significant variations in customer preferences among the brands.
Hypothesis Testing
6. Null Hypothesis (H0): There is no difference in brand preference among customers for the Cyan, Pearl, and Onyx brands.- (H0: \mu_{Cyan} = \mu_{Pearl} = \mu_{Onyx})
7. Alternative Hypothesis (H1): There is a difference in brand preference among customers for at least one of the brands.- (H1: \text{At least one } \mu \text{ is different})
- Level of Significance ((\alpha)): 0.10
Data Analysis
Single-Factor ANOVA
- We will perform a single-factor ANOVA test using the sales data for each brand on randomly selected days.
- The ANOVA test will help us determine if there are statistically significant differences in brand preferences among customers.
Results
8. F Test Statistic: The F test statistic from the ANOVA output will indicate the ratio of the variance between groups to the variance within groups.
9. Decision: By comparing the calculated F test statistic with the critical value of the F test statistic at the 0.10 significance level, we will decide whether to reject or fail to reject the null hypothesis based on the level of significance and the obtained results.
Conclusion
Through a rigorous statistical analysis of brand preferences among customers at the silk shop, Moto can gain valuable insights into customer preferences and make informed decisions regarding expanding the color selection. The results of this study will provide Moto with data-driven recommendations on catering to customer needs and enhancing the shopping experience at the shop.