https://docs.google.com/spreadsheets/d/1fl9P7SVqhdQkMSp1vCk50s12TmLMWozRlnRhouR7

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https://docs.google.com/spreadsheets/d/1fl9P7SVqhdQkMSp1vCk50s12TmLMWozRlnRhouR7glY/edit#gid=424186648

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Q1) Intention to use a smartphone to purchase: Apple vs Non-Apple Users This question has several parts (a) Examine just the data relating to those who currently own or lease an Apple smartphone. Construct a confidence interval to describe the average intention to use their smartphone for purchasing products in the next month among current Apple users. (b) Examine just the data relating to those who currently do not own or do not lease an Apple smartphone. Construct a confidence interval to describe the average intention to use their smartphone for purchasing products in the next month among such users. (c) Do the confidence intervals overlap? (d) What does your answer to (c) suggest about differences in the average intentions to use the smartphone for purchasing products in the next month between those who own or lease an Apple smartphone compared to those who do not? Please note: As with all five questions, explain which variables you used as inputs into your answers In answering this question, you should clearly show the various inputs to the margin of error that you used to construct the two intervals rather than relying on any automatically generated margin of error (e.g., selecting Excel Descriptive Statistics dialogue box) which may instead be useful to check your answers. Clearly state any assumptions that you are making to undertake the question. As you have access to a computer, you will be expected to use a table-value that is accurate (not rounded). This selection of table should be based on your knowledge about the population parameters, which you should also state to justify your selection of table. Present any inputs and answers to two decimal places, but round your calculations only at the end though to avoid round error.

Explanation / Answer

From the given data, there are 177 Apple users and 223 non-Apple users.

(a) Analysing the Apple user data in an ordered way (low to high) for intention to use the smartphone to purchase products next month, we have the mean = 2.59, Mode = 1, standard deviation = 1.478.

The 95% confidence interval corresponds to 1.96 times S.D. around mean

1.96 X 1.478 = 2.897. So the confidence interval is [2.59-2.897, 2.59+2.897], i.e., [-0.307,5.487]. Since negative values are not allowed, we have the 95% confidence interval as [0,5.487]

(b) Similarly analysing the non-Apple user data, we have mean = 3.51, Mode = 1, Standard Deviation = 1.858

1.96 X S.D. = 1.96 X 1.858 = 3.6417

So the 95% confidence interval is [3.51-3.641, 3.51+3.641], i.e., [-0.131,7.151]. Since values less than 0 and greater than 7 have no meaning, so the 95% confidence interval covers the entire sample space [0,7].

(c) The 95% confidence intervals for the average intention to use their smartphone for purchasing products in the next month among Apple and non-Apple users do overlap.

(d) The intention to use smartphone for purchasing products in the next month is more likely for non-Apple users as their preferences are well spread-out with many responses of value 7 (Very likely). Also, the average value of the intention for non-Apple users is higher at 3.51, compared to 2.59 for Apple users. So the non-Apple users are more likely to have the intention to use smartphone for purchasing products in the next month.

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