Question

The manufacturer of a certain candy states that 15% of the candies are brown, 15% yellow, 25% red, 20% blue, 10% orange, 15% green. A student randomly selected a giant bag of candy and counted the number of each color. The results are in the table below. Does the candy follow the stated distribution?

(a) Complete the table. Report all answers accurate to 2 decimal places.

Color	Brown	Yellow	Red	Blue	Orange	Green
Frequency	21	23	24	26	7	16
Expected Frequency

(b) Select the null and alternative hypotheses.

• H0H0: The colors are independent
  HaHa: The colors are dependent
• H0H0: PBr=PY=PR=PBl=PO=PG=16PBr=PY=PR=PBl=PO=PG=16
  HaHa: at least one proportion is different
• H0H0: PBrPBr=0.15, PYPY=0.15, PRPR=0.25, PBlPBl=0.20,POPO=0.1,PGPG=0.15,
  HaHa: at least one proportion is different

(c) What is the chi-square test-statistic for this data? Round your answer to 3 decimals.
χ2=χ2=

(d) What is the P-Value? Round your answer to 4 decimals.
P-Value =


(e) For significance level alpha 0.01, what would be the decision of this hypothesis test?

• Fail to reject the Null Hypothesis
• Reject the Null Hypothesis

(f) Select the conclusion.

• There is not sufficient evidence to support that the claim that at least one proportion is different. Therefore, the candy follows the stated distribution
• There is sufficient evidence to support the claim that at least one proportion is different. Therefore, the candy does not follow the stated distribution.

Answer 1

The statistical software output for this problem is :

H0H0: PBr=0.15, PY =0.15, PR =0.25, PB =0.20,PO =0.1,PG = 0.15,
Ha at least one proportion is different .

χ2 = 7.461

P-value = 0.1885

Fail to reject the Null Hypothesis

There is not sufficient evidence to support that the claim that at least one proportion is different. Therefore, the candy follows the stated distribution