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A large supermarket carries four qualities of ground beef. Customers are believed to purchase these four...

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Statistics

A large supermarket carries four qualities of ground beef.Customers are believed to purchase these four varieties withprobabilities of 0.13, 0.27, 0.14, and 0.46, respectively, from theleast to most expensive variety. A sample of 480 purchases resultedin sales of 48, 148, 74, and 210 of the respective qualities. Doesthis sample contradict the expected proportions? Use α =0.05.

(a) Find the test statistic. (Round your answer to two decimalplaces.)


(ii) Find the p-value. (Round your answer to four decimalplaces.)

A program for generating random numbers on a computer is to betested. The program is instructed to generate 100 single-digitintegers between 0 and 9. The frequencies of the observed integerswere as follows. At the 0.05 level of significance, is theresufficient reason to believe that the integers are not beinggenerated uniformly?

Integer0123456789
Frequency1086813107111413

(a) Find the test statistic. (Round your answer to two decimalplaces.)


(ii) Find the p-value. (Round your answer to four decimalplaces.)

Answer & Explanation Solved by verified expert
3.7 Ratings (296 Votes)

1)

           relative observed Expected Chi square
category frequency(p) Oi Ei=total*p R2i=(Oi-Ei)2/Ei
1 0.13 48.0 62.40 3.323
2 0.27 148.0 129.60 2.612
3 0.14 74.0 67.20 0.688
4 0.46 210.0 220.80 0.528
total 1.000 480 480 7.1518
test statistic X2 = 7.15

ii)

p value = 0.0672

2)

applying chi square goodness of fit test:
           relative observed Expected residual Chi square
category frequency(p) Oi Ei=total*p R2i=(Oi-Ei)/√Ei R2i=(Oi-Ei)2/Ei
0 0.10 10.0 10.00 0.00 0.000
1 0.10 8.0 10.00 -0.63 0.400
2 0.10 6.0 10.00 -1.26 1.600
3 0.10 8.0 10.00 -0.63 0.400
4 0.10 13.0 10.00 0.95 0.900
5 0.10 10.0 10.00 0.00 0.000
6 0.10 7.0 10.00 -0.95 0.900
7 0.10 11.0 10.00 0.32 0.100
8 0.10 14.0 10.00 1.26 1.600
9 0.10 13.0 10.00 0.95 0.900
total 1.000 100 100 6.8000
test statistic X2 = 6.80
ii) p value = 0.6579
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