A manufacturer has come up with a new and improved type of top-of-the-line radial tires. They think that these new tires will last longer, on average, than the current average of 42,000 km, under normal driving conditions. A random sample of 8 tires yielded the following lifetime mileages (in km): 42,500 42,400 41,900 42,200 42,100 41,800 42,600 42,300

Tire lifetime mileage is normally distributed. From the sample evidence, can the manufacturer conclude that the new tires will last longer than 42,000 miles? Test at = 5%. Answer the following questions:

(a) What would be the value of the test statistic? (in 2 decimal places)

(b) What would be the critical value? (in 3 decimal places)