15) Use the provided randomization distribution (based on 100 samples) to test i

Question

15) Use the provided randomization distribution (based on 100 samples) to test if this sample provides the proportion of candies that are green differs for the two types of M&M;'s. Include 15) an assessment of the strength of your evidence. 50 40 30 20 10 .0.20 .0.15 .0.10-0.05 0.4c 0.05 0.10 0.15 0.20 0.25 null 0 A) 0.06 B) 0.10 C) 0.16 D) 0.32 16) Use your p-value to make a decision about these hypotheses using a -0.05. Be sure to word your decision in the context of the problem. Include an assessment of the strength of your evidence. 16) A) Do not reject Ho. this p-value provides evidence that the proportion of green candies differs B) Reject Ho this p-value provides evidence that the proportion of green candies differs for milk C) Reject Ho, this p-value provides no evidence that the proportion of green candies differs for D) Do not reject H0, this p-value provides no evidence that the proportion of green candies for milk chocolate and dark chocolate M&M;'s chocolate and dark chocolate M&Ms; milk chocolate and dark chocolate M&M;'s differs for milk chocolate and dark chocolate M&M;'s. atch each p-value to the most appropriate conclusion. 17) The evidence against the null and in favor of the alternative is very strong 17) A) 0.07 B) 0.04 C) 0.65 D) 0.0001 18) The result is significant at the 5% level but not at a 1% level. 18) A) 0.04 B) 0.65 ) 0.07 D) 0.0001 19) There is really no evidence supporting the alternative hypothesis 0.0001 19) A) 0.07 B) 0.65 D) 0.04 20) The evidence against the null is significant, but only at the 10% level B) 0.04 20) C) 00001 D) 0.07 A) 0.65

Explanation / Answer

15)

The sample mean proportion is 0.0095

The standard deviation is 0.096

The standard error of the sample mean is 0.096 / sqrt(100) = 0.0096

P[p > 0.0095] = P[z > (0.0095 - 0)/0.0096] = P[z > 0.9896]

= 0.16

For two tail hypothesis, P-value = 2 * P[p > 0.0095] = 2 * 0.16 = 0.32

Hence the correct answer is D) 0.32

16)

As, p-value is greater than significance level of 0.05,
D) Do not reject H0, this p-value provides no evidence that the proportion of green candies differs for milk chocolate and dark chocolate M&Ms.

17)
The p-value in favor of the alternative is p-value which is close to 0 (minimum of all). So, the correct answer is,
D) 0.0001

18)
The result is significant at 5% and 1% level is p-value between 0.01 and 0.05. So, the correct answer is,
A) 0.04

19)
No evidence supporting the alternative hypothesis is highest p-value
B) 0.65

20)
Evidence against the null hypothesis only at 10% level (an not at 5% level), is p-value which is between 0.05 and 0.1
D) 0.07

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