02402 · Exercise Quiz 6

In the production of a certain foil (film), the foil is controlled by measuring the thickness of the foil in a number of points distributed over the width of the foil. The production is considered stable if the mean of the difference between the maximum and minimum measurements does not exceed 0.35mm. At a given day, the following data are found for 10 foils:

Foil	1	2	3	4	5	6	7	8	9	10
Max. measurement in mm ($y_{max}$)	2.62	2.71	2.18	2.25	2.72	2.34	2.63	1.86	2.84	2.93
Min. measurement in mm ($y_{min}$)	2.14	2.39	1.86	1.92	2.33	2.00	2.25	1.50	2.27	2.37
Max-Min($D$)	0.48	0.32	0.32	0.33	0.39	0.34	0.38	0.36	0.57	0.56

The following statistics may potentially be used: \(\bar{y}_{max}=2.508,\;\bar{y}_{min}=2.103,\;s_{y_{max}}=0.3373,\;s_{y_{min}}=0.2834,\;s_{D}=0.09664\)

If the following hypothesis test on the mean difference is carried out:

\[\begin{array}{l} {H_0}:{\mu_D} = 0.35\\ {H_1}:{\mu_D} \not= 0.35 \end{array}\]

The critical value for the t-test of the hypothesis on level $\alpha=0.01$ is: (expressed by R-functions)