Question

Question 1
(a) In a metal fabrication process, metal rods are produced that have an average length of
20.5 feet with a standard deviation of 2.3 feet. A quality control specialist collects a random
sample of 30 rods and measures their lengths.
(i) Describe the sampling distribution for the sample mean by naming the model and telling its
mean and standard deviation. [3 marks]
(ii) Calculate the probability that the sample mean length of metal rods is less than 19.5 feet.
[2 marks]
(b) 47 packages are randomly selected from packages received by a parcel service. The sample
has a mean weight of 25.6 pounds and a standard deviation of 2.8 pounds. What is the 95 percent
confidence interval for the true mean weight, μ, of all packages received by the parcel service?
Interpret your answer. [5 marks]
Total 10 marks

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

Question 3
A manufacturer considers his production process to be out of control when defects exceed 3%. In
a random sample of 85 items, the defect rate is 5.9% but the manager claims that this is only a
sample fluctuation and production is not really out of control. At the 0.01 level of significance,
test the manager's claim.
(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) Determine the critical region(s) for this test. [2 marks]
(d) State the conclusion of this test. Give a reason for your answer. [3 marks]
Total 10 marks

Question 4
The table below shows the age and favourite type of music of 668 randomly selected people.

	Rock	Pop	Classical
1525	50	85	73
25-35	68	91	60
35-45	90	74	77

Use a 5 percent level of significance to test the null hypothesis that age and preferred music type
are independent.
(a) State the null and alternative hypotheses for this test. [2 marks]
(b) Calculate:
(i) the expected frequency, E21, for age 25-35 years and favourite music is Rock
(ii) the chisquare contribution, χ2, for age 25-35 years and favourite music is Rock
given that the chi-square test statistic, χ2, is 12.954, find the p-value for test
[3 marks]
(c) State the conclusion for the test. [3 marks]
(d) State 2 limitations of the chi-square test, χ2.

Answer 1

Let us answer question 1. For this we find the mean and standard deviation of the sample distribution and find the probability using them. The solution is as shown below.