Homework Problem 10.23 (v5) or none (v7): A newspaper article discussed the open

Question

Homework Problem 10.23 (v5) or none (v7): A newspaper article discussed the opening of a Whole Foods Market in the Time-Warner building in New York City. The following data (stored in the file WHOLEFOODS1) compared the price of some kitchen staples at the new Whole Foods Market and at the Fairway supermarket located about 15 blocks from the Time-Warner Building. At the.01 level of significance, is there evidence that the mean price is higher at Whole Foods Market than at the Fairway supermarket? (In order to answer this question you MUST complete the 6 steps.) a) b) Report the p-value in (a) and interpret it's meaning c) What assumption is necessary about the population distribution in order to perform the test in (a)?

Explanation / Answer

Here we have to test the hypothesis that,

H0 : mu1 = mu2 Vs H1 : mu1 > mu2

where mu1 is the population mean for whole foods and

mu2 is the population mean for fairway.

Assume alpha = level of significance = 0.01

Here sample size is too small and sample data is given so we use two sample t-test assuming equal variances.

We can do two sample t-test in excel.

steps :

ENTER data into excel sheet --> Data --> Data analysis --> t-test : Two sample assuming equal variances --> ok --> Variable 1 Range : seelct whole foods data range --> Variable 2 Range : select fairway data range --> Hypothesized mean difference : 0 --> Click on Labels --> Alpha : 0.01 --> Output Range : Select one empty cell --> ok

Test statistic = 0.85

P-value = 0.2027

P-value > alpha

Accept H0 at 1% level of significance.

Conclusion : There is not sufficient evidence to say that the mean price is higher at whole foods market than at the fairway supermarket.

We get insignificant result about t-test.

Assumption :

Sample size is of 10 which is less than 30 and population standard deviation is unknown so we use two sample t-test.

t-Test: Two-Sample Assuming Equal Variances Whole Foods Fairway Mean 2.92 2.24 Variance 4.080133 2.288911 Observations 10 10 Pooled Variance 3.184522 Hypothesized Mean Difference 0 df 18 t Stat 0.852063 P(T<=t) one-tail 0.202687 t Critical one-tail 2.55238 P(T<=t) two-tail 0.405374 t Critical two-tail 2.87844

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