Research New Zealand conducts monthly telephone surveys in which they survey a sample of adult New Zealanders, aged 18 years or over. You may assume these surveys use simple random sampling.

The December 2016 survey sampled 272 adult New Zealanders and included a question designed to measure the opinions of adult New Zealanders on moving the summer holiday period from December to February. This question was also asked in their December 2014 and December 2015 surveys. (ResearchNZ, 20162).

The question asked in each survey was:

Do you believe New Zealand should move its summer holiday period from December to February when the weather is warmer?

A summary of the answers to this question for the three years is shown in the table below:

Year

2016 Total 98 528 152 642 22 102 272 1272

(a) State the sampling situation for analysing the difference between the estimated proportion of adult New Zealanders, aged 18 years or over who, in December 2014, believed New Zealand should move its summer holiday period from December to February when the weather is warmer and the estimated proportion of adult New Zealanders, aged 18 years or over who, in December 2016, believed New Zealand should move its summer holiday period from December to February when the weather is warmer. [ 1 mark ]

(b) Carry out a t-test to investigate whether there is a difference between the underlying proportion of adult New Zealanders, aged 18 years or over who, in December 2016, believed New Zealand should move its summer holiday period from December to February when the weather is warmer and the underlying proportion of adult New Zealanders, aged 18 years or over who, in December 2016, did not believe New Zealand should move its summer holiday period from December to February when the weather is warmer. [ 8 marks ]

Notes:

(i) You must clearly show that you have followed the "Step?by?Step Guide to Performing a

Hypothesis Test by Hand" given in the Lecture Workbook, Chapter 7, blue page 14.

(ii) At Steps 5 and 8, it is necessary to use the t?procedures tool on Canvas (Assignments >

Assignment 3) to determine the standard error and the t?multiplier.

(iii) At Step 6, it is necessary to use the t?procedures tool on Canvas to determine the P?value.

(iv) Refer to the instructions on page 1 of this assignment: "Hypothesis tests in this assignment".

Research New Zealand conducts monthly telephone surveys in which they survey a sample of adult New Zealanders, aged 18 years or over. You may assume these surveys use simple random sampling. The December 2016 survey sampled 272 adult New Zealanders and included a question designed to measure the opinions of adult New Zealanders on moving the summer holiday period from December to February. This question was also asked in their December 2014 and December 2015 surveys. (ResearchNZ, 20162). The question asked in each survey was: Do you believe New Zealand should move its summer holiday period from December to February when the weather is warmer? A summary of the answers to this question for the three years is shown in the table below: Year Answer 2014 2015 2016 Total Yes 240 190 98 528 No 225 265 152 642 Don't know 35 45 22 102 Total 500 500 272 1272 (a) State the sampling situation for analysing the difference between the estimated proportion of adult New Zealanders, aged 18 years or over who, in December 2014, believed New Zealand should move its summer holiday period from December to February when the weather is warmer and the estimated proportion of adult New Zealanders, aged 18 years or over who, in December 2016, believed New Zealand should move its summer holiday period from December to February when the weather is warmer. [ 1 mark ] Carry out a t-test to investigate whether there is a difference between the underlying proportion of adult New Zealanders, aged 18 years or over who, in December 2016, believed New Zealand should move its summer holiday period from December to February when the weather is warmer and the underlying proportion of adult New Zealanders, aged 18 years or over who, in December 2016, did not believe New Zealand should move its summer holiday period from December to February when the weather is warmer. [ 8 marks ]