Tiny ball bearings are produced by an aerospace company. The diameters of these ball bearings can be reasonably assumed to be normally distributed. All ball bearings produced are supposed to have a...

Tiny ball bearings are produced by an aerospace company. The diameters of these ball bearings can be reasonably assumed to be normally distributed. All ball bearings produced are supposed to have a diameter of 3.5 mm. The manager of the production is concerned that the mean is higher than it should be. The following random sample of seven ball bearings had diameters in mm of:

3.1   4.9   3.6   4.5   3.7   4.2   5.1

Conduct a test for the manager to determine if there is significant evidence that the mean diameter of all ball bearings produced is more than 3.5 mm at the 5% significance level.