Many people believe that they experience "information overload' in today's digital world. A report describes
a survey in which people were asked if they feel overloaded by information. Suppose in a representative
sample of 634 college graduates, 102 indicated that they suffered from information overload, while
119 people in an independent representative sample of 496 people who had never attended college said
that they suffered from information overload.
Construct a 95% large-sample confidence interval for the proportion of college graduates who
experience information overload
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To construct a large-sample confidence interval for the proportion of college graduates who experience information overload, we can use the formula:
CI = p̂ ± Z * √(p̂(1-p̂)/n)
Where:
CI = Confidence Interval
p̂ = Sample proportion
Z = Z-score for the desired level of confidence
n = Sample size
First, we calculate the sample proportion for college graduates:
p̂1 = 102/634 = 0.1609
Next, we calculate the Z-score for a 95% confidence level. For a 95% confidence level, the Z-score is approximately 1.96.
Z = 1.96
Finally, we calculate the confidence interval using the formula:
CI = 0.1609 ± 1.96 * √(0.1609(1-0.1609)/634)
CI = 0.1609 ± 1.96 * √(0.1359/634)
CI = 0.1609 ± 1.96 * 0.0112
CI = 0.1609 ± 0.0219
The 95% large-sample confidence interval for the proportion of college graduates who experience information overload is (0.1390, 0.1828).
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