Question

Question 2
The health of employees is monitored by periodically weighing them in. A sample of 54
employees has a mean weight of 183.9 lb. Assuming that σ is known to be 121.2 lb, use a 0.10
significance level to test the claim that the population mean of all such employees weights is less
than 200 lb.

(a) State the null and alternative hypotheses for the test. [3 marks]

(b) Calculate the value of the test statistic for this test. [2 marks]

(c) Calculate the p-value for this test. [2 marks]

(d) State the conclusion of this test. Give a reason for your answer. [3 marks]
Total 10 marks

Answer 1

a)

H0: >= 200

Ha: < 200 (Claim)

b)

Test statistics

z = - / ( / sqrt(n) )

= 183.9 - 200 / (121.2 / sqrt(54) )

= -0.98

This is test statistics value.

c)

P value = P( Z < z)

= P( Z < -0.98)

= 0.1635

d)

Since p-value > 0.10 significance level, we do not have sufficient evidence to reject H0.

We conclude at 0.10 level that we fail to support the claim.