When doing your demographic research on smartphone usage for Tech Solutions, you

Question

When doing your demographic research on smartphone usage for Tech Solutions, you found that in a random sample of 100 eighteen to thirty-five year olds, 87 used a smartphone. In a random sample of 100 individuals who are age thirty-six or older, 56 were found to use smartphones.

1. Use these data to compute a 95% confidence interval for the difference between the population proportion of eighteen to thirty-five year olds who use smartphones, and the population proportion of individuals age thirty-six and older who use smartphones. Make sure to clearly indicate which calculator interval you are computing, and show that you checked the necessary conditions for inference.

2. Does the interval from part a consist of all positive numbers, all negative numbers, or a mix of both? At the 95% level of confidence, is there an age-based difference in the proportion of people who use smartphones

PS: Please include written explanation of how its done, if possible. Thanks much!

Explanation / Answer

Calculating confidence interval for difference in means,

For your sample, 87 out of 100 is 0.87 The 95% CI for that is from 0.79 to 0.92
For reference data, 56 out of 100 is 0.56 The 95% CI for that is from 0.46 to 0.65

The 95 % CI for the difference is from 0.19 to 0.42

b) Z score is 4.8559

p-value is less than 0.0004, which is significant at the 95% confidence level since it is less than 0.05

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