Question

Samples              Normal Papel    Construction Papel         With Staple

1            3.55       4.72       3.96

2            4.02       6.52       3.16

3            4.16       5.06       3.38

4            4.88       5.25       4.25

5            4.16       5.64       3.40

6            4.40       5.75       3.31

7            3.80       5.50       3.96

8            4.30       4.98       4.25

9            3.98       5.02       4.09

10          3.96       3.98       3.76

11          3.93       4.20       3.83

12          4.15       4.96       3.70

13          3.88       4.72       4.00

14          4.42       4.62       3.86

15          4.25       3.46       4.32

16          4.50       4.46       4.53

17          4.28       4.34       3.09

18          4.13       4.36       3.46

19          4.28       5.08       3.76

20          4.26       5.02       3.86

Interval Plot of Papel, Construction 95% CI for the Mean 5.2 5.0 4.8 3 4.6 4.4 4.2 4.0 Papel ndividual standard deviations are used to calculate the intervals Construction

Explain the interval plot above.

Answer 1

These plot indicates the 95% confidence interval for Normal papel and construction papel respectively

The blue dot indicates respective means

Normal papel :

Mean = ( 3.55 + 4.02 + 4.16 + 4.88 + 4.16 + 4.40 + 3.80 + 4.30 + 3.98 + 3.96 + 3.93 + 4.15 + 3.88 + 4.42 + 4.25 + 4.50 + 4.28 + 4.13 + 4.28 + 4.26 ) / 20 = 4.1645

Var = sum( value - mean )^2 / (n-1) = 0.082

Standard deviation = SD = 0.286

95% confidence interval is given by :

mean +/- SD*z(0.05)/(n^0.5) = 4.1645 +/- ( 0.286*1.96 )/20^0.5 = 4.1645 +/- 0.125 = ( 4.0395, 4.2895 )

For, Normal papel the line represents all the values between ( 4.0395, 4.2895 ) and dotted point is 4.1645

Construction papel :

Mean = ( 4.72 + 6.52 + 5.06 + 5.25 + 5.64 + 5.75 + 5.5 + 4.98 + 5.02 + 3.98 + 4.20 + 4.96 + 4.72 + 4.62 +  3.46 + 4.46 + 4.34 + 4.36 + 5.08 + 5.02 ) / 20 = 97.64 / 20 = 4.882

Var = sum( value - mean )^2 / (n-1) = 1.581

Standard deviation = SD = 1.257

95% confidence interval is given by :

mean +/- SD*z(0.05)/(n^0.5) = 4.882 +/- ( 1.257*1.96 )/20^0.5 = 4.882 +/- 0.551 = ( 4.331, 5.433 )

For, Construction papel the line represents all the values between ( 4.331, 5.433 ) and dotted point is 4.882

Note: the variance of construction papel is more than that of normal papel, therefore it has greater 95% confidence interval hence, longer line in graph.