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rosijanka [135]
3 years ago
7

A math teacher was frustrated at the number of students leaving their graphing calculator behind in her classroom at the end of

class without a way to locate the student. A random sample of 50 students is selected, and of the students questioned, 32 had their names written on their graphing calculators.
Required:
What would be a 99% confidence interval for the proportion of all students at this school who have their names written on their graphing calculators?
Mathematics
1 answer:
AleksAgata [21]3 years ago
8 0

Answer:

The 99% confidence interval for the proportion of all students at this school who have their names written on their graphing calculators is (0.4652, 0.8148).

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

A random sample of 50 students is selected, and of the students questioned, 32 had their names written on their graphing calculators.

This means that n = 50, \pi = \frac{32}{50} = 0.64

99% confidence level

So \alpha = 0.01, z is the value of Z that has a pvalue of 1 - \frac{0.01}{2} = 0.995, so Z = 2.575.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.64 - 2.575\sqrt{\frac{0.64*0.36}{50}} = 0.4652

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.64 + 2.575\sqrt{\frac{0.64*0.36}{50}} = 0.8148

The 99% confidence interval for the proportion of all students at this school who have their names written on their graphing calculators is (0.4652, 0.8148).

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