Mathematics: A 5 quart carton of juice costs $8.40. What is the cost per pint.

The 98% confidence interval for the true population proportion of all New York students who favor year round school is (0.3083, 0.4383).Step-by-step explanation:In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.In whichz is the z-score that has a p-value of .A survey of 300 students from a New York State School District reveals that 112 favor year round school with two week vacations...

A 5 quart carton of juice costs $8.40. What is

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Rflaig1129841

16.05.2020

Mathematics

The 98% confidence interval for the true population proportion of all New York students who favor year round school is (0.3083, 0.4383).

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 level of $1-\alpha$ , we have the following confidence interval of proportions.

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

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

A survey of 300 students from a New York State School District reveals that 112 favor year round school with two week vacations every ten weeks.

This means that $n = 300, \pi = \frac{112}{300} = 0.3733$

98% confidence level

So $\alpha = 0.02$ , z is the value of Z that has a p-value of $1 - \frac{0.02}{2} = 0.99$ , so Z = 2.327 .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3733 - 2.327\sqrt{\frac{0.3733*0.6267}{300}} = 0.3083$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3733 + 2.327\sqrt{\frac{0.3733*0.6267}{300}} = 0.4383$

The 98% confidence interval for the true population proportion of all New York students who favor year round school is (0.3083, 0.4383).

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A 5 quart carton of juice costs $8.40. What is the cost per pint.

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