A large survey in the USA establishes that 60 per cent of its residents own a smartphone.
A survey of 250 UK residents reveals that 164 of them own a smartphone.
Assuming that these 250 UK residents may be regarded as a random sample, investigate the claim that the percentage of UK residents owning a smartphone is the same as that in the USA. Use the 5\% level of significance.
A random sample of 40 residents in a market town reveals that 5 of them own a 4 G mobile phone.
Use an exact test to investigate, at the \(5 \%\) level of significance, the belief that fewer than 25 per cent of the town's residents own a 4 G mobile phone.
A marketing company needs to estimate the proportion of residents in a large city who own a 4 G mobile phone. It wishes to estimate this proportion to within 0.05 with a confidence of 98\%.
Given that the proportion is known to be at most 30 per cent, estimate the sample size necessary in order to meet the company's need. [0pt]
[5 marks]