Use the data in the table to the right to answer the following questions Find th

Question

Use the data in the table to the right to answer the following questions Find the sample proportion of candy that are red The proportion of red candy- Weights (g) of a Sample Bag of Candy Red 897 0.986 0.972 0 808 0.829 0.793 0 726 0.797 0.774 0 702 0892 0 763 Yellow 0.979 0.915 0.772 0 831 0872 0 807 0 921 0717 0.905 0.914 0.821 745 (Type an integer or decimal rounded to three decimal places as needed) Use that result to construct a 95% confidence interval estimate of the population percentage or candy that are red 0.705 0 863 0712 0.894 0.716 0714 0986 0.708 0.927 0 848 0 848 0.983 0 318 0 991 0.741 0.937 Type an integer or decimal rounded to one decimal place as needed.) Istre resut consistent with the 30% rate that is reported by the candy maker? 0.858 0.962 No, because the confidence interval does not include 3096. yes, because the confidence interval includes 30% O

Explanation / Answer

TRADITIONAL METHOD
Q1.
given that,
possibile chances, number of red candy, (x)=10
sample size, total umber of candy, (n)=48
the proportion of red candy = success rate ( p )= x/n = 0.2083

Q2.
I.
sample proportion = 0.2083
standard error = Sqrt ( (0.2083*0.7917) /48) )
= 0.0586
II.
margin of error = Z a/2 * (stanadard error)
where,
Za/2 = Z-table value
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
margin of error = 1.96 * 0.0586
= 0.1149
III.
CI = [ p ± margin of error ]
confidence interval = [0.2083 ± 0.1149]
= [ 0.0934 , 0.3232]
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DIRECT METHOD
given that,
possibile chances (x)=10
sample size(n)=48
success rate ( p )= x/n = 0.2083
CI = confidence interval
confidence interval = [ 0.2083 ± 1.96 * Sqrt ( (0.2083*0.7917) /48) ) ]
= [0.2083 - 1.96 * Sqrt ( (0.2083*0.7917) /48) , 0.2083 + 1.96 * Sqrt ( (0.2083*0.7917) /48) ]
= [0.0934 , 0.3232]
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interpretations:
1. We are 95% sure that the interval [ 0.0934 , 0.3232] contains the true population proportion
2. If a large number of samples are collected, and a confidence interval is created
for each sample, 95% of these intervals will contains the true population proportion

Q3.
yes, because the confidence interval includes 30%

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