A certain electro-optical firm currently uses a laser component in producing sophisticated graphic designs. The time it takes to produce a particular design with the current laser component is known to follow a normal distribution, with a population mean of 70 seconds and a known population standard deviation of 4 seconds. The firm is now trying to decide whether they purchase a relatively expensive new laser component. If, it can be shown that it takes significantly less time, on the average, to produce the particular design using the new laser component, then the firm will go ahead with the purchase.

The firm takes a random sample of 8 designs produced using the new laser component and finds that the production time (in seconds) for each as follows:

64, 61, 61, 55, 61, 62, 72, 69

Can we conclude that the firm should purchase the new laser component? Use a 10% level of significance.

How would we work this out?