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svp [43]
3 years ago
15

Suppose a sample of 80 with a sample proportion of 0.58 is taken from a population. Which of the following is the approximate 95

% confidence interval for the population parameter?
Mathematics
2 answers:
elena55 [62]3 years ago
6 0

Answer:

The 95% confidence interval for the population parameter is (0.4718, 0.6882).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence interval 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

Z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

For this problem, we have that:

n = 80, p = 0.58

95% confidence interval

So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so z = 1.96.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.58 - 1.96\sqrt{\frac{0.58*0.42}{80}} = 0.4718

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.58 + 1.96\sqrt{\frac{0.58*0.42}{80}} = 0.6882

The 95% confidence interval for the population parameter is (0.4718, 0.6882).

Sveta_85 [38]3 years ago
3 0

Answer:

Correct answer is 0.470 0.690.  

Step-by-step explanation:

Just got it right on apex.

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