Answer:
Step-by-step explanation:
To construct a confidence interval for the population proportion (pp), you can use the following formula:
Confidence Interval=p^±z×p^(1−p^)nConfidence Interval=p^±z×np^(1−p^)
Where:
p^p^ is the sample proportion (in this case, x/nx/n),
zz is the critical value corresponding to the desired confidence level,
nn is the sample size.
Given that x=160x=160, n=200n=200, and you want a 90% confidence interval, you'll need to find the critical value for a 90% confidence level. You can refer to the table of critical values or use statistical software.
Assuming you find z=Zα/2z=Zα/2 for a 90% confidence level, you substitute the values into the formula.
Confidence Interval=160200±Zα/2×160200×(1−160200)200Confidence Interval=200160±Zα/2×200200160×(1−200160)
Calculate the values to find the lower and upper bounds of the confidence interval.
Please note that Zα/2Zα/2 for a 90% confidence level is approximately 1.645.
Confidence Interval=160200±1.645×160200×(1−160200)200Confidence Interval=200160±1.645×200200160×(1−200160)
Now, compute the numerical values to get the lower and upper bounds. Make sure to round to three decimal places.
Confidence Interval≈0.8±1.645×0.8×0.2200Confidence Interval≈0.8±1.645×2000.8×0.2
After calculating this expression, you'll obtain the lower and upper bounds of the 90% confidence interval for the population proportion.