Question

Construct a 90% confidence interval of the population proportion using the given information. x=160,n=200 Click here to view the table of critical values. The lower bound is The upper bound is (Round to three decimal places as needed.)

Answer 1

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^​)​

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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​)​

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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​)​

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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​

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After calculating this expression, you'll obtain the lower and upper bounds of the 90% confidence interval for the population proportion.