Question

In: Statistics and Probability

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)

  1. H0:
  2. Ha:
  3. T. S.:
  4. R (Draw Rejection region with the critical value)
  5. 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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