Question

Use the data below to create a 99% confidence interval of the average population price of all 200 gram bags of candy. Include all work that supports your answer. ( 10 points) Note this question is only using the "item price " variable. (Not the quantity sold variable). The “200 grams” is added just to make the amount per bag constant (but it does not factor into the calculation). Show calculations in Excel.

Item Price / 200g

2.25

1.29

2.35

1.39

1.33

1.4

1.44

2.99

1.45

1.1

3.1

77

1.25

2.5

2

1.69

2.15

1.99

2.25

Answer 1

Mean X̅ = Σ Xi / n
X̅ = 110.92 / 19 = 5.8379

Sample Standard deviation SX = √ ( (Xi - X̅ )2 / n - 1 )
SX = √ ( 5351.6207 / 19 -1 ) = 17.2427

Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.01 /2, 19- 1 ) = 2.878
5.8379 ± t(0.01/2, 19 -1) * 17.2427/√(19)
Lower Limit = 5.8379 - t(0.01/2, 19 -1) 17.2427/√(19)
Lower Limit = -5.5485
Upper Limit = 5.8379 + t(0.01/2, 19 -1) 17.2427/√(19)
Upper Limit = 17.2243
99% Confidence interval is ( -5.5485 , 17.2243 )

Excel output
  
99%   confidence level
5.837894737   mean
17.2427452   std. dev.
19   n
2.878   t (df = 18)
11.3864    half-width
17.2243    upper confidence limit
-5.5485    lower confidence limit