Question 3. (19)

The weights of school bags for secondary school students have mean, m = 4 kilograms with a standard deviation, s = 1 kilogram. A random sample of 30 students are selected from a school to determine the sample mean, x .

1. What is the value of E(x ) and sx ? Explain your answers. (3)

2. What is the probability that the mean weight of bag from a sample of 30 students is greater than 4.5 kilograms? (3)

3. What is the confidence interval at 5% significance level? Interpret your answer. (4)

Confidence interval at 5% significance level:

4. What is the confidence interval at 10% significance level? How is your answer different from answer in part (c)? (4)

5. The Ministry of Education claims that students time tables are well designed that students do not carry many books to school every day. If weight of school bags are not to be greater than 4 kilograms, do a hypothesis testing on MoEs claim, at 5% significant level based on the sample mean. (5)