Question

2. M&M’s are delicious. “They melt in your mouth, not in your hand.” According to the M&M’s company, their most popular color is blue.

(a) You open regular pack of M&M’s find that 14 of the 80 candies are red. Construct and interpret a 95% confidence interval for the proportion of red M$M’s candies.

(b) N&N’s is another candy company selling candy coated chocolates. Their slogan is “They melt where it’s warm, so put them in your mouth.” They are being sued by M$M’s for copyright infringement. In their defense, the N$N’s company claims that their proportion of blue candies is much larger than 24% (the proportion for blue M$M’s). As an expert witness, you pick a random sample of N&N’s candies and found 71 out of 240 were blue. Does this provide statistically significant evidence for N&N’s claim?

Answer 1

2.

(a)

Formula for confidence interval for population proportion: p

Number of red candies in a regular pack of M & M : x=14

Total number of candies : n = 80

Sample proportion of red M& M candies : = 14/80 = 0.175

for 95% confidence level = (100-95)/100 = 0.05

/2 = 0.05/2=0.025

Z/2 = Z0.025 = 1.96

95% confidence interval for the proportion of red M$M’s candies

95% confidence interval for the proportion of red M$M’s candies = (0.091736,0.258264)

With 95% confidence we can say that the proportion of red M$M’s candies is between 0.091736 and 0.258264

(b)

p: proportion of blue candies in  N$N’s

N$N’s company claims that their proportion of blue candies is much larger than 24% i.e p > 0.24

Null hypothesis : Ho : p = 0.24

Alternative Hypothesis : Ha : p > 0.24

Hypothesized proportion : po = 0.24

Number of candies randomly sampled : n= 240

Number of blue candies in the sample : x = 71

Sample proportion of blue candies : = 71/240 = 0.2958

Test Statistic :

For right tailed test :

P-Value = P(Z>Zstat) = P(Z>2.0241) = 1-P(Z<2.0241)=1-0.9785=0.0215

For 5% level of significance : i.e = 0.05

As P-Value i.e. is less than Level of significance i.e (P-value:0.0215 < 0.05:Level of significance); Reject Null Hypothesis
At 5% level of significance There is sufficient evidence to conclude that  proportion of blue candies is larger than 24%

For 1% level of significance : i.e = 0.01

As P-Value i.e. is less than Level of significance i.e (P-value:0.0215 >  0.01:Level of significance); Fail to Reject Null Hypothesis
At 1% level of significance There is not sufficient evidence to conclude that  proportion of blue candies is larger than 24%

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As at 1% level of significance There is not sufficient evidence to conclude that  proportion of blue candies is larger than 24% ; This does not  provide statistically significant evidence for N&N’s claim