22. Consumer Behaviour (15 Marks} hlarket research companies are often interested in establishing the level of demand for new products. For this question, you are to place yourself in the shoes of a researcher who is trying to: (i) obtain a representative sample of the underlying population who may be interested in buying a new mobile phone, and (ii) analyse the data such that you can gauge the level of interest for this product. In order to gather data on interest in buying this phone, you will need a sampling plan. What method of sampling (simple random, stratied, cluster) will you use in this instance? Give a brief justification of your choice. In analysing your data, you are likely to encounter both sampling error and nonsampling error. Which do you think will be a greater threat to your analysis? Give an example of how nonsarnpling error may bias your results. The tile rrrobiles.xls has data on 100 randomly selected individuals. The column labelled ifemrf indicates whether or not that individual has expressed some interest in buying your new product. A value of 1 here indicates that the individual is interested while a value of zero indicates that they are not. Calculate the fraction of the sample that is interested in the new brand of mobile m: @ express this value as a percentage. Suppose you need 30% of your target population to be interested in order to be successful. Do you think the new product will be a success? 'Why or why not? Determine the standard error for the sample proportion reported in the point my use this to calculate a 95% condence interval for the true population proportion (hint you can use the Excel spreadsheet tab categorical_CI.Xls for this). On the basis of this interval, do you believe your phone will be successful? As condence intervals become wider, they become more likely to contain the true population parameter, and hence become more amnufe. On the other hand, wider intervals are less useful, as they are less prams. Write a couple of sentences contrasting the benefits of a wider interval vs a narrower interval. Using the tab \"hypothesis test\" in your Excel le, test the null that the population proportion is equal to 0.3. Give the null and alternative hypothesis, test statistic, critical value and a conclusion. Use a significance level of 50/0 and interpret your result