Final answer:
To construct a 90% confidence interval estimate for the population proportion of consumers who value personalized experience most when shopping in a retail store, we can use the formula CI = p' +/- Z * sqrt((p' * (1 - p')) / n). Plugging in the values, we find a confidence interval of approximately 0.236 to 0.304. Therefore, we can estimate that with 90% confidence, the population proportion of consumers who value personalized experience most is between 23.6% and 30.4%.
Step-by-step explanation:
To construct a confidence interval estimate for the population proportion, we can use the formula:
CI = p' ± Z * sqrt((p' * (1 - p')) / n)
where:
- CI is the confidence interval
- p' is the sample proportion
- Z is the Z score for the desired confidence level
- n is the sample size
In this case, the sample proportion is 27% (0.27), the sample size is 800, and the desired confidence level is 90%. The Z score for a 90% confidence level is approximately 1.645. Plugging these values into the formula, we get:
CI = 0.27 ± 1.645 * sqrt((0.27 * (1 - 0.27)) / 800)
Calculating this, we find the confidence interval to be approximately 0.236 to 0.304. Therefore, we can estimate that with 90% confidence, the population proportion of consumers who value personalized experience most when shopping in a retail store is between 23.6% and 30.4%.