Question

Use the given degree of confidence and sample data to construct a confidence interval for the population mean µ. 31 packages are randomly selected from packages received by a parcel service. The sample has a mean weight of 15.7 pounds and a standard deviation of 1.7 pounds. What is the 95 percent confidence interval for the true mean weight, µ, of all packages received by the parcel service?

(15.2, 16.2) (14.9, 16.5) (15.0, 16.4) (15.1, 16.3)

Answer #1

Solution :

Given that,

sample size = n = 31

Degrees of freedom = df = n - 1 = 31 - 1 = 30

t_{
/2,df} = 2.042

Margin of error = E = t_{/2,df}
* (s /n)

= 2.042 * (1.7 / 31)

Margin of error = E = 0.6

The 95% confidence interval estimate of the population mean is,

- E < < + E

15.7 - 0.6 < < 15.7 + 0.6

15.1 < < 16.3

**(15.1 , 16.3)**

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