Question

I need help with computing minitab.

Minitab table given (refered to as Data:Current.mtw in the question)

Phosphorus Type	Glass Type	Current uA
1	1	280
1	1	290
1	1	285
2	1	300
2	1	310
2	1	295
3	1	290
3	1	285
3	1	290
1	2	230
1	2	235
1	2	240
2	2	260
2	2	240
2	2	235
3	2	220
3	2	225
3	2	230

1. An article in Industrial Quality Control (1956, pp. 5-8) describes an experiment to investigate the effect of the type of glass and the type ofphosphor on the brightness of a television tube. The response variable is the current necessary (in microamps) to obtain a specified brightness level. 1290 285 285 290 310 295 230 260 240 235 220 225 230 2235 240 Perform a 4 C's analysis to determine if the type of glass, the type of phosphor and interaction are all significantly affecting the brightness of a television tube. (Data: currentmtw) Glass Context (4+4+4-12pts) parameters 0: a: Phosphor Type parameters Но На Interaction 0: a: Conditions (3 +3 pts) Graph Interpretation Calculations (7 pts+ 6pts) Minitab output Test statistics & p-values Glass Type Phosphor Type test statistic: Interaction. p-value- test statistic p-value p-value- test statistic: Conclusion (9 pts) Decision for all tests Glass Type Reject Ho Fail to reject Ho [circle one] Does the type of glass significantly affect the brightness of a TV tube?YES NO (circle one) Why? Phosphor Type Reject Ho Fail to reject Ho[circle one) Does the type of phosphor significantly affect the brightness of a TV tube? YES NO (circle one) Why? Interaction Reject Ho Fail to reject Ho [circle one) Is there a significant interaction affecting the brightness of a TV tube? YES NO (circle one) Why?

Answer 1

A) Context: Glass Type

$H_{0}:$ Glass Type have no effect on brightness of the Television Tube.

$H_{1}:$ Glass Type has significant effect on brightness of the Television Tube.

Context: Phosphorus Type

$H_{0}:$ Phosphorus Type have no effect on brightness of the Television Tube.

$H_{1}:$ Phosphorus Type has significant effect on brightness of the Television Tube.

Context: Interactive effect of both Glass Type and Phosphorus Type

$H_{0}:$ Interactive effect of both Glass Type and Phosphorus Type have no effect on brightness of the Television Tube.

$H_{1}:$ Interactive effect of both Glass Type and Phosphorus Type has significant effect on brightness of the Television Tube.

B) The Graph is given below.

Residual Plots for Current uA Normal Probability Plot Versus Fits 90 10 10 10 10 220 240 260 Residual Fitted Value Versus Order Histogram 10 10 -10-5 10 15 2 4 68 10 12 14 16 18 Residual Observation Order

The data is approximately normal and residuals plots shows that residual are randomly distributed.

c) The results in the said format

Source	Test Statistics	DF1	DF2	P.Value
GlassType	273.79	1	12	0.000
Phosphorus Type	8.84	2	12	0.004
Interaction	1.26	2	12	0.318

and ANOVA table is given below

Source	DF	SS	MS	F	P.Value
Glass Type	1	14450	14450	273.79	0.000
Phosphorus Type	2	933.3	466.7	8.84	0.004
Interaction	2	133.3	66.7	1.26	0.318
Error	12	633.3	52.8
Total	17	16150

d) Glass Type : Since P.Value = 0.000 which is less then 0.05 therefore we reject H₀ and conclude that Glass Type has significant effect on brightness of the Television Tube.

Phosphorus Type: Since P.Value = 0.004 which is less then 0.05 therefore we reject H₀ and conclude that phosphorus Type has significant effect on brightness of the Television Tube.

Interaction: Since P.Value = 0.318 which is greater then 0.05 therefore we accept H₀ and conclude that Interactive effect of both Glass Type and Phosphorus Type have not significant effect on brightness of the Television Tube.