Answer:
The 90% confidence interval for the proportion of married couples with three personality preferences in common compared with the proportion of couples with two preferences in common is (-0.081, 0.025).
Step-by-step explanation:
The (1 - α)% confidence interval for difference in proportion formula is,
The given information is:
n₁ = 375,
n₂ = 571,
X₁ = 132,
X₂ = 217.
Compute the sample proportion as follows:
For the 90% confidence level, the z-value is,
z₀.₀₅ = 1.645
*Use a z-table.
Compute the 90% confidence interval for the difference in proportion as follows:
The 90% confidence interval for the proportion of married couples with three personality preferences in common compared with the proportion of couples with two preferences in common is (-0.081, 0.025).
This confidence interval implies that the true difference between the proportions lies in this interval with probability 0.90.
