Chip Jap Limited (CJL), a Japanese microchip manufacturer had concerns about the efficiency of its microchip machine. Based on the documentation of the microchip machine, CJL should be producing on average 38 microchips per day. Nine random samples were collected with the following averages: 25; 32; 38; 28; 36; 23; 42; 43; 21.

Assume that the population distribution is normal. Test at the 5% confidence level againts a two-sided alternative.

a) Formulate the null and alternative two-tailed hypotheses.

b) Calculate the sample mean.

c) Calculate the sample standard deviation.

d) What are the critical values using a significance level of 5%?

e) Calculate the test statistic.

f) Based on your answers to parts (d) and (e) above, provide a response to CJL whether the microchip machinery is operating within the manufacturer specification.

g) Explain two facts about the level of significance.