Question

Suppose a sample of​ O-rings was obtained and the wall thickness​ (in inches) of each was recorded. Use a normal probability plot to assess whether the sample data could have come from a population that is normally distributed.		0.1900.190	0.1850.185	0.2020.202	0.2040.204
		0.2090.209	0.2140.214	0.2270.227	0.2380.238
		0.2550.255	0.2650.265	0.2770.277	0.2890.289
		0.3040.304	0.2980.298	0.3050.305	0.3160.316

Answer 1

Below 2 models are provided one using Excel and other using Minitab software, Kindly refer any one but not both because you may landup confused if you refer both.

P value has different roles while using in Excel and in Minitab, Both are not same please note.

In excel I have considered p value as per Regression analysis and in Minitab I have considered p value as per Hypothesis testing.

But both are one at the same.

Answer: Arrange the observations in smaller to larger order, Calculate probability and Expected thickness readings as per the formula provided.

Rank	Observed Wall Thickness(Inches)	Probability=(Rank-0.5)/n	Expected Wall Thickness(=Norminv(Probability,Mean,Stdev))
1	0.185	0.03125	0.164
2	0.190	0.09375	0.189
3	0.202	0.15625	0.203
4	0.204	0.21875	0.213
5	0.209	0.28125	0.222
6	0.214	0.34375	0.230
7	0.227	0.40625	0.238
8	0.238	0.46875	0.245
9	0.255	0.53125	0.252
10	0.265	0.59375	0.259
11	0.277	0.65625	0.267
12	0.289	0.71875	0.275
13	0.298	0.78125	0.284
14	0.304	0.84375	0.295
15	0.305	0.90625	0.309
16	0.316	0.96875	0.333

Mean	0.248625
STDEV	0.045435

Graph using Excel-Scatter plot between observed and expecetd values

Calculation Using Excel:

Regression Statistics
Multiple R	0.970315507
R Square	0.941512184
Adjusted R Square	0.937013121
Standard Error	0.010143388
Observations	15
ANOVA
	df	SS	MS	F	Significance F
Regression	1	0.021531286	0.021531	209.2685137	2.15702E-09
Residual	13	0.001337548	0.000103
Total	14	0.022868835
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	0.026968845	0.015929249	1.693039	0.114259313	-0.007444204	0.061381895	-0.007444204	0.061381895
0.185	0.898886487	0.062137376	14.46612	2.15702E-09	0.764646848	1.033126126	0.764646848	1.033126126

Path to access:(Data Analysis>Regression>Enter Y as Expected values and X as Observed values>OK)

Here the p value is very much less than 0.05 hence it is significant, If the value is greater than 0.05 then it is non significant.

Plot using Minitab Software:

Consider H0=Null Hypothesis: Data follows Normal distribution

H1=Alternate Hypothesis: Data doesn't follow Normal distribution.

P value from graph is 0.203 which is greater than 0.05(The significance level), Hence we fail to reject the Null Hypothesis.

By this we can say that the sample data is following the Normal distribution that means it is drawn from a Normally distributed data.

(Path to access Probability plot in Minitab: Graph>Probability Plot>Single>Select the colimn with data points)