Question

Comparing Grocery Prices Consumer groups often analyze store prices and compare the price of similar items in different stores. They share this information with other consumers or customers. Imagine that a consumer group suspects that there is a difference in prices between two grocery stores (Store A and Store B). To investigate, the consumer group identifies the prices of six identical items at Stores A and B. Since prices change over time, the consumer group gathers all data on a single day. The consumer group's data is shown in the table below. At the 5% level of significance, is there enough evidence to conclude that a difference exists between the prices of grocery items in the two stores? Assume the population of price differences is normally distributed. All prices are in dollars. Cheese Napkins Bread Juice Milk Product Eggs 3.59 2,99 3.49 2.89 2.59 3.29 Store A 3.19 3.99 2.69 3.79 3.99 2.99 Store B Step 1: Determine the Hypotheses Are the data paired? Explain. 1 State the null and alternative hypotheses. Assume that we find differences as Store B price minus Sto 2 A price. Is this a right-tailed, left-tailed, or two-tailed test? 3 Step 2: Collect the Data Are the criteria for approximate normality met for the sampling distribution of differences? 4 Determine the following: The mean of the sample differences, The standard deviation of the sample differences, and The number of data pairs in the sample, n. Is the mean of sample differences consistent with your alternative hypothesis? 6 Step 3: Assess the Evidence Calculate the test statistic for your observed mean of sample differences. 7 Sketch the T-distribution. Identify the position of the observed test statistic. Shade the area that 8 represents the P-value. LO 9 Use the test statistic to determine the P-value. Step 4: State a Conclusion 10 How does the P-value compare to the significance level? Should we reject or fail to reject the null hypothesis? 11 What can we conclude about the alternative hypothesis? 12 State a conclusion in context.

Answer 1

collect store prices of similar items in two different stores A and B so 1. Since we the data is paired 2. Let d Но Ha 3. Two tail test. 4. true average difference price of grocery items in Store A and Store B

Probability Plot of Difference=Store A-Store B Normal 95% CI 99 Mean -0.3 StDev 0.2683 N AD 0.609 P-Value 0.059 70 60 50 40 30 20 10 1 -1.5 -1.0 -0.5 0.0 0.5 1.0 Difference-Store A-Store B Percent 8 R 9n

From above plot and p-value>0.05 so the criteria for approximate normality is met.

5. Mean of the sample differences d 0.300 Mean of the sample differences Sd 0.268 n 6 6. Yes since Mean of the sample differences < 0 Vnd 2.74 7. Test statistic Sd

8.

-2.74 2.74 2 0 1 2 3

p value 2P(t > 2.74 t 10. Since p value < 0.05 so we 11. Accept Ha 12. There is enough evidence to conclude that a difference exists between the prices of grocery items in the two stores. t6)= 0.041 reject Ho.