A worker randomly selects 16 packages from all the holiday packages received at

Question

A worker randomly selects 16 packages from all the holiday packages received at a local parcel service. The sample has a mean weight of 16.4 pounds and a standard deviation of 3.3 pounds. Assume that the weights of holiday packages are known to be approximately normally distributed.

a. What is the point estimate for the true mean weight, µ, of all holiday packages received by the parcel service?

b. Calculate an interval estimate for the true mean weight, µ, of all packages received by the parcel service. In other words, construct a 90% confidence interval for the true mean weight, µ, of all packages received by the parcal service.

c. How many holiday packages must be randomly selected if we want 95% confidence that the sample mean weight is within 0.5 pounds of the population mean weight?

Explanation / Answer

a. mean = xbar = 16.4

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b. a=0.1, t(0.05, df=n-1=15)= 1.75 (check student t table)

SO 90% CI is
xbar ± t*s/n

--> 16.4 ± 1.75*3.3/4

--> (14.95625, 17.84375)
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c. a=0.05, t(0.025, df-15)=2.13

E=0.5

So n=(t*s/E)^2 = (2.13*3.3/0.5)^2 = 197.6274

Take n= 198

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