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on september 16, 2011, the new york times reported that the american public's approval rating of congress had sunk to an all-time low of 12%. if this were regarded as true for the population, and a poll two weeks later of 500 individuals found a proportion of 14%, we can find the value of the z test statistic using the formula: . what is the simplified numerator? please type the correct answer in the following input field, and then select the submit answer button or press the enter key when finished.

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To estimate the percentage of people who at that time approve of Congress to within 3% at 95% confidence, 451 people must be surveyed.

According to the problem:

The sample size is 451, with n.

Margin of error is E=0.03

Sample Proportion P=0.12

The confidence level from the question is 95%, hence the level of significance is,

[tex]\alpha=(100-95)\%[/tex]

[tex]\alpha=5\%[/tex]

[tex]\alpha=0.05[/tex]

The critical value of, according to the normal distribution table,

[tex]\alpha/2[/tex] is,

[tex]\frac{Z\alpha}{2} =1.96[/tex]

The sample size is also mathematically denoted by the following:

[tex]n=\frac{Z_\alpha/2}{E} \times\hat{p}(1-\hat{p})[/tex]

[tex]n=(\frac{1.96}{0.03}) ^2\times0.12(1-0.12)[/tex]

[tex]n=451[/tex]

In order to determine the percentage of people who approve of Congress at that time to within 3% at 95% confidence, 451 people must be surveyed.

Any properly distributed data with any potential value for its parameters the mean and the standard deviation are represented by a normal distribution, which is a type of general distribution. The standard normal distribution, on the other hand, is a special example where the mean equals zero and the standard deviation is the unit. Because of this, we are able to use the terms normal distribution and standard normal distribution.

Learn more about Normal distribution:

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