Question

QUESTION 6 (1 + 2 + 1 + 2 + 2 + 2 = 10 marks)

Please note that each part of this question is independent

1. Leather shoes are examined by an inspector in a Melbourne factory and each pair is classified as either perfect or defects. A sample of 350 pairs is randomly taken. 200 pairs are produced by Machinist A and 150 pairs by Machinist B. 8 of the pairs produced by machinist A are found to be defective while 13 of those produced by Machinist B are found to be defective. If we wish to test if the quality of workmanship depends on the machinist, what assumption do you need to make to conduct the hypothesis test?

2. “If the 95% confidence interval does not contain the hypothesised parameter, then a hypothesis test at the 0.05 level will almost always reject the null hypothesis in a two-tailed test”. Do you agree with this statement? Explain.

3. The organising committee of the carnival are of the opinion that 75% of visitors purchase a showbag. What method of assigning probabilities is used in this case? Explain.

4. If all other factors remain the same, how do the following changes affect the width of the confidence interval estimate of the population mean?
   1) Decrease in sample size
   2) Decrease in sample mean

5. A business which sells flowers and gifts through internet sales believes that the overall proportion of website hits from which sales result is 9.8%. At the 5% level they wish to test if there is evidence of decreased internet sales rate due to COVID19. The hypotheses statements for this test are:

   H₀: π ≥ 9.8%

   H₁: π < 9.8%.

   Interpret the power of the test in the context of the question.

6. How does a decrease in the significance level of a test impact the power of the test? Explain.

Answer 1

a). Assumptions:

• The samples are independent.
• n1p̂1(1-p̂1) >= 10 and n2p̂2(1-p̂2) >= 10
• The sample size is less than 5% of the population size for each sample.

b).

Yes we agree with this statement.

c).

Answer: Subjective probability.

Subjective Probability of an event is a "best guess" by a person making the statement of the chances that the event will happen.

d).

1) Decrease in sample size increases the width of the confidence interval.

2) Decrease in sample mean Does not change the width of the confidence interval.

e)

Power of the test is making the correct decision.

Rejecting the null hypothesis when it is false.

In the context of this question power will be to conclude that proportion of website hits decreases due to COVID19 when in reality it actually decreased.

f) Decrease in the significance level , decreases the power of the test.