Question

Question 4​

It may be assumed that the length of nails produced by a particular machine is a normally distributed random variable with mean 4.62cm. We have collected the following random sample of lengths of nails: 4.63 cm, 4.59 cm, 4.64 cm, 4.62 cm, 4.66 cm and 4.69 cm.

a) Find the standard error of the sample mean .

b) What is the sampling distribution of ? State any assumptions you need to make.

c) What is the probability that we observe this sample mean or a higher value?

d) What would the sampling distribution be if the nails produced by this machine are not normally distributed? What would you suggest?

Answer 1

a) Find the standard error of the sample mean .

4.63833	mean Data
0.03430	std. dev.
0.01400	std. error
6	n
5	df

The standard error of the sample mean is 0.014.

b) What is the sampling distribution of ? State any assumptions you need to make.

The sampling distribution is:

Mean = 4.63833

Standard deviation = 0.014

c) What is the probability that we observe this sample mean or a higher value?

The probability is 0.1237.

d) What would the sampling distribution be if the nails produced by this machine are not normally distributed? What would you suggest?

The distribution will be the Wilcoxon rank test.