Question

Lindsey wishes to estimate the average retail value of the 1000’s of greeting cards she has in her store inventory. A random sample of 16 cards yielded an average, X-bar = $4.67, with a sample standard deviation of s = $0.32. Find a 95% confidence interval for the true average retail value of the greeting cards in the store’s inventory.

Answer 1

Solution :

Given that,

= 4.67

s =0.32

n = Degrees of freedom = df = n - 1 =16 - 1 = 15

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t /2,df = t0.025,15 =2.131 ( using student t table)

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

= 2.131 * (0.32 / 16)

= 0.17

The 95% confidence interval is,

- E < < + E

4.67 - 0.17 < <4.67 + 0.17

4.5 < < 4.84

( 4.5 , 4.84)