(Correct your answers to 4 decimal places.) The internal quality control of a company claims that over 80% of its notebook weigh lighter than 1.3 kg. To test this claim, a random sample of 40 notebooks is selected and the weight (kg) of each notebook is recorded as follow:

1.23 1.32 1.28 1.19 1.33 1.27 1.21 1.25 1.27 1.25 1.27 1.28 1.27 1.29 1.31 1.28 1.25 1.28 1.32 1.19 1.22 1.26 1.24 1.31 1.28 1.32 1.27 1.29 1.28 1.27 1.23 1.28 1.26 1.20 1.22 1.27 1.25 1.29 1.27 1.26

Use the above data to test the claim at 5% significance level.

(a) Use p to denote the population proportion of notebook weigh lighter than 1.3 kg. Write down the null hypothesis and the alternative hypothesis of the test. (2 marks)

(b) State the rejection region of the test. (2 marks)

(c) Calculate the test statistics. (4 marks) (d) Is there sufficient evidence to conclude that over 80% of the notebooks weigh lighter than 1.3 kg? (2 marks)