The candy Reese's Pieces comes in three different colors: orange, yellow, and brown. The target color...

The candy Reese's Pieces comes in three different colors: orange, yellow, and brown. The target color distribution is 45% of the pieces orange. 27.5% yellow, and 27.5% brown. A random sample of Reese's Pieces packages contained 400 pieces having the following color distribution: 162 were orange, 117 yellow, and 121 brown.

Test the hypothesis that Reese's Pieces is meeting its target color distribution. Use α = .01 (define the population parameter(s) in H₀). (Which hypothesis is your claim)

H₀:
H_a:
T. S.:
R (Draw Rejection region with the critical value)
Conclusion:

Based on your test of hypothesis, which statement would you agree with (choose one)?

__________ Reese's Pieces is probably meeting its target color distribution.

__________ Reese's Pieces is probably not meeting its target color distribution.

6. Approximate the p-value for your test statistic in part a) using the χ²

7. Suppose the maximum value of α that you are willing to tolerate is .10. What would be your conclusion?

Another way to obtain a p-value is through computer simulation. Use the statistical program StatKeyto obtain a p-value for your test statistic in part a) (see directions).

Solutions

Expert Solution

Ho: Reese's Pieces is probably meeting its target color distribution
Ha: Reese's Pieces is probably not meeting its target color distribution

level of significance, α=   0.01
Degree of freedom=k-1=   3   -   1   =   2



Critical value =    9.210   [ Excel function: =chisq.inv.rt(α,df) ]
reject Ho if test stat > 9.210

observed frequencey, O	expected proportion	expected frequency,E	(O-E)	(O-E)²	(O-E)²/E
162	0.450	180.00	-18.00	324.00	1.800
117	0.275	110.00	7.00	49.00	0.445
121	0.275	110.00	11.00	121.00	1.100

chi square test statistic,X² = Σ(O-E)²/E = 3.345

since, test stat < 9.210, fail to reject Ho

Reese's Pieces is probably not meeting its target color distribution

6) P value = 0.1877 [ excel function: =chisq.dist.rt(test-stat,df) ]

7) conclusion wil remain same, Reese's Pieces is probably not meeting its target color distribution

orchestra answered 1 year ago

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