A National Retailer routinely collects data on their customer preferences for level of varieties in sweater colors. A survey is designed and delivered to customers whether they prefer: no variety (1 color only), low variety (2-3 colors), medium variety (4-6 colors) and high variety (more than 7 colors) .

The first round of the survey (survey pilot just to obtain baseline estimates), delivered in 2012, determines the following distribution (empirical frequencies) for preferences for variety:

No variety: 25%

Low variety: 20%

Medium Variety: 35%

High Variety: 20%

This pilot study was conducted on a very large sample, so that it is safe to ignore any uncertainty related to these point estimates for proportions.

A follow up survey was administered in 2016 and delivers the following results:

No variety: 45%

Low variety: 15%

Medium Variety: 25%

High Variety: 15%

Total number of customer surveyed in 2016: 3500

The retailer is interested in understanding whether the preference for variety in their customer base has changed in the last 4 years. We ought to apply a formal testing procedure to solve this dilemma.

1) what are the hypothesis?

2) We must assess whether the sample size is adequate. Specifically, we need to check min(np ₀ , np _1, ..., n p _k ) > 5. The sample size here is n= ____and the proportions specified in the null hypothesis are ____, ____, _____, _____

Thus, min( ….(….), …..(….), …..(….), …..(….))=min(…., …., …., …..)=….. The sample size is (is not) adequate, so the formula can (cannot) be used

3) what is the decision rule?

4) what is the test statistic?

	No Variety	Low Variety	Medium Variety	High Variety	Total
Observed Frequencies (O)
Expected Frequencies (E)