NZ On Air commissioned a survey called "New Zealand's Identity, Culture and the Media. What's changed in 30 years?". This study included a review of a 1990 survey and a new survey in August, 2019. The information below is based on the 2019 survey results. Assume the survey is a random sample of New Zealand adults. Some of the results are shown below:

Respondents were asked to identify their preferred television/online programmes. Information on their first preference of programme type, classified by age, are:

Programme type Under 50 50+ Total

Drama 193 192 385

Comedy 291 76 367

Documentaries 161 157 318

Investigative journalism/

Current affairs 95 139 234

Reality/lifestyle shows 91 42 133

Animation 62 5 67

Children's programmes 36 0 36

No preference 45 40 85

Don't know 20 15 35

Total 994 666 1660

The same respondents were asked to identify all the services they used to watch the programmes

they liked. Results, classified by age, are: Under 50 50+ Total

Service (n=994) (n=666) (n=1660)

Free to view TV (e.g. TVNZ1, Three, Prime) 659 553 1212

Online video (e.g. Facebook, YouTube, Vimeo) 663 284 947

A paid streaming service (e.g. Lightbox, Neon) 609 238 847

On demand, from a free to view TV channel 454 293 747

Live on a Sky TV channel 255 260 515

Sky on demand (Sky Go) 112 54 166

Torrent site(s) (e.g. The Pirate Bay, EZTV) 102 31 133

None of the above 37 13 50

(a)State the sampling situation (a, b or c) for calculating the standard error of the difference in the following scenarios:

(i)estimating the difference between the proportion of people under 50 who watch programs on Torrent sites and the proportion of people 50 or over who watch programs on Torrent sites.

(ii)estimating the difference between the proportion of people who used Live on a Sky TV channel to watch the programmes they liked and the proportion of people who used Sky on demand to watch the programmes they liked.

(iii)estimating the difference between the proportion of people whose first preference of programme type was investigative journalism/current affairs and the proportion of people whose first preference of programme type was reality/lifestyle shows.

[3 Marks]

(b)Calculate and interpret a 95% confidence interval for the difference between the proportion of people under 50 who would watch programmes they liked on online videos and the proportion of people under 50 who would watch programmes they liked on a paid streaming service. [6 Marks]

Note: You must clearly show that you have followed the "Step-by-Step Guide to Producing a Confidence Interval by Hand" given in the Lecture Workbook, Chapter 6. Use the t-procedures tool to find values for the t-multiplier and standard error.