Solution:
Reese’s candies manufactured by Hershey
Sample distribution of colors of the candies is 25 and Reese’s pieces come in three colors that is
orange, brown and yellow
Colors of the candies and proportion drawn from each colors candies
Orange is 10/25 = 0.4 proportion
Yellow is 10/25 = 0.4 proportion
Brown is 5/25 = 0.2 proportion
1) In a sample of 25 Reese’s pieces, when counting the number of orange candies randomly.
We got proportion of orange candies is 0.4 because orange is 10 out of 25 candies.
Therefore, 10/25 = 0.4
2)
a) The proportion of orange candies among the 25 candies of sample is a statistic because
the proportion of orange candies we got is based on a sample. Thus the values are our
estimates for the parameter. The proportional values that we got above are describing a
sample of candies that is drawn from the true population. Therefore, the value is called
a statistic
b) The proportion of orange candies manufactured by Hershey’s is a parameter because
parameter is based on population data.
c) The best estimates of the true population proportion are 0.4 based on sample that is
P  =0.4 because sample is our estimates of the population proportion of orange
candies.
d) No, we do not suspect that every person in the class obtained the same proportion of
orange candies. Sample is a statistic and it is drawn randomly. So it changes every
time we draw a sample. For example if another classmate draws 15 orange candies out
of the 25 is drawn randomly from the sample. The proportion of 0.6 we would get and
if this process will continue with other classmates the proportion we would get is
different. Therefore, we exactly do not expect that every classmates have the same
value of estimates would derived.
e) If everyone in the class estimates the population proportion of orange candies with the
proportion of orange candies in their sample have same estimates, because the
estimates are the true proportion of orange candies on the basis of all the values of
sample proportion the student have. This implies that to estimates the parameter we
use the mean proportion of the sample.
Virtual sample
Random sample of Reese’s pieces it is either the 25 0r 30 as sample size and it clearly refers the
large sample size.
Use of java applet for this question to answer, I need an application to run the sample estimates.
Therefore, let me explain what the result is likely to be on the basis of statistics.
So, when we lake large sample and repeat the process of estimates again and again, we get
efficient estimator which is close to the population parameter.
In the process of repetition, we get some sample proportion is greater than 0.45 for the orange
candies and some proportion is less than that value of 0.45, to get efficient estimates which is
close to our population parameter, we required to get the mean of all the sample proportion.
Mean and standard deviation to compare with true parameter in the each simulation would be
different but should not vary more to our true population parameter of 0.45
Discussion prompt
n = 50
1. The proportion found in our physical sample is s x =.03
2. Based on the data a histogram format, the distribution of data is approximately normal
because the data shows a bell shaped.