Hypothesis testing

Your number is S 3 6 2 1 1 3 2 Your Year of birth is 1 9 9 6 You will make some numbers usin" rel="nofollow">ing your student number The first number, to be used in" rel="nofollow">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" rel="nofollow">in Question 2. It is made from the last two digits in" rel="nofollow">in your student number Now referred as B 3 2 The Third number will be used Question 3, and is made usin" rel="nofollow">ing the third and fourth digits of your student number Now referred as C 2 1 The nin" rel="nofollow">ine 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" rel="nofollow">in your year of birth added together List the 9 numbers you will be usin" rel="nofollow">ing in" rel="nofollow">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 min" rel="nofollow">ints in" rel="nofollow">in a packet are supposed to be 120 with a standard deviation 2.4. A lot of complain" rel="nofollow">ints 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 min" rel="nofollow">ints. 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 in" rel="nofollow">interpret your answer (6 marks) b) What is the p-value? ( 1 mark) 2) The Waitin" rel="nofollow">ing time for a Pizza order is supposed to be no more than 10 min" rel="nofollow">inutes. Some complain" rel="nofollow">ints have been received that the orders are in" rel="nofollow">in fact takin" rel="nofollow">ing longer than the claimed 10 min" rel="nofollow">inutes. A batch of B orders was timed and found to have an average order time of 10.9 min" rel="nofollow">inutes and a sample standard deviation of (A ÷ 40 ) min" rel="nofollow">inutes. Prepare a hypothesis test to test whether the orders are takin" rel="nofollow">ing longer than 10 min" rel="nofollow">inutes. Test at 1% significance. Test whether the null hypothesis usin" rel="nofollow">ing critical value H0 : μ ≤ 10 should be accepted or rejected. Be sure to in" rel="nofollow">interpret your answer (6 marks) 3) The proportion of people who love dogs is known to be 75 % Australia wide. A town in" rel="nofollow">in far north Queensland is often different in" rel="nofollow">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 makin" rel="nofollow">ing a type 1 error is 5%. Use critical value for testin" rel="nofollow">ing the hypothesis. Be sure to in" rel="nofollow">interpret your answer ( 6 marks) b) What is the p-value? ( 1 mark) 4) A batch of pain" rel="nofollow">int tin" rel="nofollow">ins was thought to be of irregular volume. The tin" rel="nofollow">ins are labelled as bein" rel="nofollow">ing 16 litres A batch of 9 tin" rel="nofollow">ins was measured for their contents. The followin" rel="nofollow">ing volumes in" rel="nofollow">in litres were found. You will be usin" rel="nofollow">ing data set D Given the probability of a type 1 error is 0.01, test whether or not the tin" rel="nofollow">ins are in" rel="nofollow">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 testin" rel="nofollow">ing= 10marks). 5) You will need to write a paragraph answer to one of the followin" rel="nofollow">ing questions in" rel="nofollow">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 kin" rel="nofollow">ind ( 7 marks) b) Your friend is not sure how to use the Z tables to fin" rel="nofollow">ind 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 fin" rel="nofollow">ind 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" rel="nofollow">in hypothesis testin" rel="nofollow">ing? Give some examples (7 marks) e) α = 0.05 and α = 0.01 are the most common significance levels used in" rel="nofollow">in Hypothesis testin" rel="nofollow">ing. Describe what it means to do a test at either of these levels of significance (7 marks)