Here are the weights in ounces of the 10 donuts the baker selected. 4.7 3.6 2.5 3.7 4.6 3.6 4.9 3.2 3.2 3.4The sample mean for these data is ?̅ = 3.74 ounces. The dotplot below shows the distribution of the sample mean weight of a donut for 500 random samples of size 10 taken with replacement from the original sample. Export this graph3.5Simulated sample mean of weight of donutsDistribution of Simulated Mean# samples meanSD5003.763 0.2284.5(a) Use the results of the simulation to approximate the margin of error for the estimate ofthe mean weight of the donuts (ounces).(c) Interpret the margin of error.

The following information has been provided: The sample size is n=500. The sample mean is x¯=3.763. The sample standard deviation is S=0.228a.) The formula for margin of error is : MOE=Zc.σn The critical value of z can be computed using the EXCEL formula at α=0.05. Zc=NORM.S.INVprobability =NORM.S.INVα2 =NORM.S.INV0.052 =NORM.S.INV0.025 =1.96 MOE=Zc.σn =1.96 .0.228500 =0.02 The margin of error is 0.02. b.) The margin of error describe the amount of sampling error present in the result. It gives the percentage value which shows the variation in the result that differ from the original population value. According to the above result we interpret that a 95% confidence interval with a 2% margin of error suggests that your statistic will, 95% of the time, be within 2% of the true population value.

Answered: Distribution of Simulated Mean SD 0.228…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Here are the weights in ounces of the 10 donuts the baker selected.
4.7 3.6 2.5 3.7 4.6 3.6 4.9 3.2 3.2 3.4

The sample mean for these data is ?̅ = 3.74 ounces. The dotplot below shows the distribution of the sample mean weight of a donut for 500 random samples of size 10 taken with replacement from the original sample.

Export this graph
3.5
Simulated sample mean of weight of donuts
Distribution of Simulated Mean
# samples mean
SD
500
3.763 0.228
4.5
(a) Use the results of the simulation to approximate the margin of error for the estimate of
the mean weight of the donuts (ounces).
(c) Interpret the margin of error.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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