https://docs.google.com/spreadsheets/d/1fl9P7SVqhdQkMSp1vCk50s12TmLMWozRlnRhouR7
ID: 3253417 • Letter: H
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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
Look for brand column
1---Apple
count apple users=27
sample proportion=27/400=0.0675
z for 95%=1.96
95% confidence interval for population proportion of users who own smartphone currently is
sample proportion+-margin of error
margin of error=z sqrt[p(1-p)/n]
=1.96 sqrt[0.0675(1-0.0675)/400]
=0.0246
lower limit=sample proportion-margion of error
=0.0675-0.0246
=0.0429
upper limit=sample proportion+margion of error
=0.0675+0.0246
=0.0921
we are 95% confident that population proption of apple users lies in between
0.0429 and 0.0921
in percentages=0.0429*100=4.29% and
0.0921*100=9.21%
Solution:
400-27=373not apple users
proportion of non apple users=p^=373/400=0.9325
95% Confidence inteval is
0.9325-1.96 sqrt[.09325(1-.9325)/400],0.9325+1.96 sqrt[.09325(1-.9325)/400]
0.9325 -0.0246, 0.9325 +0.0246
0.9079,0.9571
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