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WITCHER [35]
3 years ago
15

A statistic instructor randomly selected four bags of oranges, each bag labeled 10 pounds, and weighed the bags.They weighed 9.3

, 9.7, 9.2, and 9.7 pounds. assume that the distribution of the weights is normal. Find a 95% confidence interval for the mean weight of all bags of oranges.
We are 95% confident the population mean is between ____ and ____?
Mathematics
1 answer:
____ [38]3 years ago
3 0

Answer:

95% confident the population mean is between (9.1,9.9)

Step-by-step explanation:

We are given the following data set:

9.3, 9.7, 9.2, 9.7

Formula:

\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}  

where x_i are data points, \bar{x} is the mean and n is the number of observations.  

Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}

Mean =\displaystyle\frac{37.9}{4} = 9.475

Sum of squares of differences = 0.2075

S.D = \sqrt{\frac{0.2075}{3}} = 0.262

95% Confidence interval:  

\bar{x} \pm t_{critical}\displaystyle\frac{s}{\sqrt{n}}  

Putting the values, we get,  

t_{critical}\text{ at degree of freedom 3 and}~\alpha_{0.05} = \pm 3.182  

9.475 \pm 3.182(\frac{0.262}{\sqrt{4}} ) = 9.475 \pm 0.416842 =(9.058158,9.891842) \approx (9.1,9.9)  

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