Hypothesis testing

3 6 2 1 1 3 2

1 9 9 6
You will make some numbers using your student number

The first number, to be used in question 1, is the first two digits of your student number Now referred as A
3 6

The second number will be used in Question 2. It is made from the last two digits in your student number
Now referred as B

3 2

The Third number will be used Question 3, and is made using the third and fourth digits of your student number
Now referred as C
2 1

The nine numbers to be used as a sample for question four are made from the digits

1 First
Digit 1 Second
Digit 1 Third
Digit 1 Fourth Digit 1 Fifth
Digit
1 Sixth
Digit 1 Seventh
Digit
96

Plus my age= 20 and The two last digits in your year of birth added together

List the 9 numbers you will be using in the box below, And this will be referred to as data set D

13 , 16 , 12 , 11 , 11 , 13 , 12 , 15

1) The contents of mints in a packet are supposed to be 120 with a standard deviation 2.4. A lot of complaints have been received that the packets are under filled. A batch of A cartons was
measured and found to have an average number of 118.3 mints. Prepare a hypothesis test to test whether the cartons are under filled or not. Test at 1% significance.
a) Test whether the null hypothesis H0: μ ≥ 120 should be accepted or rejected. Be sure to interpret your answer (6 marks)

b) What is the p-value? ( 1 mark)

2) The Waiting time for a Pizza order is supposed to be no more than 10 minutes. Some complaints have been received that the orders are in fact taking longer than the claimed 10 minutes. A
batch of B orders was timed and found to have an average order time of 10.9 minutes and a sample standard deviation of (A ÷ 40 ) minutes. Prepare a hypothesis test to test whether the orders are
taking longer than 10 minutes. Test at 1% significance.
Test whether the null hypothesis using critical value
H0 : μ ≤ 10 should be accepted or rejected. Be sure to interpret your answer (6 marks)
3) The proportion of people who love dogs is known to be 75 % Australia wide. A town in far north Queensland is often different in many aspects to the rest of Australia. When C families were
sampled the proportion who loved dogs was 68%.
a) Test whether this town is significantly different to the rest of Australia, given the probability of making a type 1 error is 5%. Use critical value for testing the hypothesis. Be sure to
b) What is the p-value? ( 1 mark)

4) A batch of paint tins was thought to be of irregular volume. The tins are labelled as being 16 litres
A batch of 9 tins was measured for their contents. The following volumes in litres were found.
You will be using data set D

Given the probability of a type 1 error is 0.01, test whether or not the tins are indeed different to the claimed 16 litres. Test whether the null hypothesis H0 : μ = 16 should be accepted or
rejected. You are required to show all your calculations of sample mean and sample standard deviation.
(1 mark for sample mean + 3 marks for sample standard deviation + 6 marks for testing= 10marks).

5) You will need to write a paragraph answer to one of the following questions in the space provided. The question you are to do depend on your student number last 2 digits B. 7 marks
If B is [0, 20) do part a)
If B is [20, 40) do part b)
If B is [40, 60) do part c)
If B is [60, 80) do part d)
If B is [80 , 100) ) do part e)

a) Describe the difference between a type I and type II error. Give an everyday example of each kind ( 7 marks)

b) Your friend is not sure how to use the Z tables to find a z value when α = 0.10 you may require a 1 tailed answer or perhaps a 2 tailed answer. Write a guide to help him ( 7 marks)

c) Your friend is not sure how to use the t tables to find a t value when α = 0.10 you may require a 1 tailed answer or perhaps a 2 tailed answer. Write a guide to help him (7 marks)

d) What is a p-value? How is it used in hypothesis testing? Give some examples (7 marks)

e) α = 0.05 and α = 0.01 are the most common significance levels used in Hypothesis testing. Describe what it means to do a test at either of these levels of significance (7 marks)