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Hypothesis Testing I
Tests for the Mean
WEEK EIGHT
This worksheet relates to chapter eight of the text book (Statistics for Managers 4 th^ Edition).
DISCUSSION QUESTIONS
- When constructing and implementing hypothesis tests, what reasoning is used behind the statement of the null and alternative hypotheses? Why are hypothesis tests set up in this way?
This topic is crucial for the final exam and for further studies. Don’t be afraid to ask questions. If you are wondering something it is likely that other people in the class are wanting to know the same thing.
- What are type one and type two errors?
A government drug regulator believes that the toxicity level in a new drug is above the industry standard and is therefore unsafe for consumers. Explain what would be a Type I and Type II error in this case. Which error would be more serious? Explain how both of these errors could be minimised simultaneously.
Complete the table of errors…
- Mr Rumpole believes that the mean income of lawyers is now more than $65 thousand per year. Which is the correct set of hypotheses to test this belief?
(a) H 0 :μ ≥ 65 000; H 1 : μ < 65 000 (b) H 0 :μ ≤ 65 000; H 1 : μ > 65 000 (c) H 0 :μ = 65 000; H 1 : μ ≠ 65 000 (d) H 0 :μ < 65 000; H 1 : μ ≥ 65 000
- Suppose a business person wishes to open a store in a local shopping centre only if there is strong evidence that the average number of people in the centre is greater than 5000 per day. The null hypothesis will be
(a) H 0 : μ ≤ 5000 (b) H 0 : μ > 5000 (c) H 0 : μ ≥ 5000 (d) H 0 : μ < 5000 (e) b or c
- If a test of a hypothesis has a type I error probability of 0.01, we mean (a) if the null hypothesis is true, we reject it 1% of the time (b) if the null hypothesis is true, we don’t reject it 1% of the time (c) if the null hypothesis is false, we reject it 1% of the time (d) if the null hypothesis is false, we don’t reject it 1% of the time Final Exam, June 2005
- In hypothesis testing
(a) rejecting the null might lead to a type II error (b) β = 1 - α (c) a type II error occurs whenever the null hypothesis is accepted (d) all of the above are incorrect Final Exam, Nov 2003
CALCULATION QUESTION
- A manufacturer of chocolate topping uses machines to dispense liquid ingredients into bottles that move along a filling line. The machine that dispenses toppings is working properly when 8 grams are dispensed. The standard deviation of the process is 0.15 gram. A sample of 50 bottles is selected periodically and the filling line is stopped if there is evidence that the average amount dispensed is actually less than 8 grams. Suppose that the average amount dispensed in a particular sample of 50 bottles is 7.983 grams.
At the 0.05 level of significance, using the critical value approach to hypothesis testing, is there evidence that the average amount dispensed is less than 8 grams?
(d) there is insufficient evidence for the manufacturer’s claim to be considered incorrect Final Exam, Nov 2003
- If a hypothesis is not rejected at the 5% level of significance is
(a) will never be rejected at the 1% level (b) will always be rejected at the 1% level (c) will sometimes not be accepted at the 1% level (d) there is insufficient information to say what will happen at the 1% level Final Exam, June 2005
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