Question

A small internet sales company decided to simplify shipping by charging the same amount for shipping on all packages. To determine the amount, they took a random sample of previous sales to determine average weight. The packages weighed (in ounces) produced the following statistics: x ¯ = 11 s = 4 . 4 n = 8 Estimate the population mean weight. Use a 95% confidence t-interval on the mean. Package weights are normally distributed. Question options:

7.32 to 14.68 oz

7.41 to 14.59 oz

7.17 to 14.83 oz

7.07 to14.93 oz

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 11

sample standard deviation = s = 4.4

sample size = n = 8

Degrees of freedom = df = n - 1 = 8-1=7

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,7 = 2.365

Margin of error = E = t/2,df * (s /n)

= 2.365 * (4.4 / 8)

Margin of error = E = 3.68

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

- E < < + E

11 - 3.68 < < 11 + 3.68

7.32 < < 14.68

(7.32,14.68) , Option 1st is correct.