A restaurant owner wants to see if his business serves the same proportion of pa

Question

A restaurant owner wants to see if his business serves the same proportion of patrons on various days of the week as other restaurants in Moscow.  He goes out and talks to all the other restaurant owners, and finds that, on average, 13% of weekly business occurs on Mondays, 17% occurs on Tuesdays, 2% occurs on Wednesdays, 23% occurs on Thursdays, 24% occurs on Fridays, 16% occurs on Saturdays, and 5% occurs on Sundays.  He decides to test these numbers against what he sees in his own business.  He finds that in his own restaurant, 7% of the business occurs on Mondays, 12% on Tuesdays, 23% on Wednesdays, 15% on Thursdays, 23% on Fridays, 19% on Saturday, and 1% on Sunday.  Is his restaurant seeing the same proportion of patrons on various days of the week as rest of the restaurants in Moscow?   Conduct a Chi-Square goodness of fit test using alpha=.05.

Explanation / Answer

H0: his restaurant seeing the same proportion of patrons on various days of the week as rest of the restaurants in Moscow

H1: his restaurant seeing the not same proportion of patrons on various days of the week as rest of the restaurants in Moscow

Given the los be alpha = 5%

The test statistic of chisquare = 231.326

The critical value of chisquare = 12.59

Here Chisquare value > Chisquare critical value , we do not accept H0.

thus we conclude that his restaurant seeing the different proportion of patrons on various days of the week as rest of the restaurants in Moscow

Oi Ei (Oi-Ei)^2/Ei 7 13 2.76923077 12 17 1.47058824 23 2 220.5 15 23 2.7826087 23 24 0.04166667 19 16 0.5625 1 5 3.2 Total: 231.326594

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