Question

Comparing Grocery Prices at Trader Joe's and Safeway.

A consumer group suspects that there is a difference in prices between Trader Joe's and Safeway. Specifically, they want to test the claim that Trader Joe's is less expensive than shopping at Safeway. To investigate this, they identified the prices of several items at both stores. Since prices change over time, all the data was gathered on a single day.

At the 5% level of significance, is there enough evidence to conclude that shopping at Trader Joe's is less expensive than shopping at Safeway? Consider Trader Joe prices to be from population 1, and Safeway prices to be from population 2.

Assume the population of price differences is normally distributed. This is not an unreasonable assumption as often prices are normally distributed. Also assume that the data represents a SRS(simple random sample) of items at the two stores.

A note on the data: Students in a prior class collected this data. I have excluded all alcohol and plant items, as the prices on these items is heavily in favor of one of the stores.

The data can be found located in the module 9 block of our reading and assignments, and also here : LINK

1) Step 1: State the Claims which means to State the null and alternative hypotheses. Use correct math type. You may want to consider looking back at the symbols assignment from the beginning of class.

Answer 1

Since except for stating the hypothesis, other information is not given, I would proceed further by just providing the hypothesis for this question :

Ho : There is no difference  in prices between Trader Joe's and Safeway i.e. mu( D ) = 0

Ha : Trader Joe's is less expensive than shopping at Safeway i.e. mu( D ) < 0

where mu(D) represents the average difference in the prices of the product.
And difference = Trader Joe's price - Safeway's price

Hope this answers your query!