Question

How much money does the average professional hockey fan spend on food at a single hockey​ game? That question was posed to 10 randomly selected hockey fans. The sampled results show that sample mean and standard deviation were

$ 11$11.00

and

$ 3.20$3.20​,

respectively. Use this information to create a

9595​%

confidence interval for the mean. Express the answer in the form

x overbar plus or minus t Subscript alpha divided by 2 Baseline left parenthesis s divided by StartRoot n EndRoot right parenthesisx±tα/2s/n.

Answer 1

Solution:

Given that,

n = 10

= 11.00

s = 3.20

Note that, Population standard deviation() is unknown. So we use t distribution.

Our aim is to construct 95% confidence interval.

c = 0.95

= 1- c = 1- 0.95 = 0.05

  /2 = 0.05 2 = 0.025

Also, d.f = n - 1 = 10 - 1 = 9

    =    =  _0.025,9 = 2.262

( use t table or t calculator to find this value..)

Confidence interval for population mean is given by

    

11.00    2.262* (3.20/10)