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slega [8]
3 years ago
7

450 high school freshmen were randomly selected for a national survey. Among survey participants, the mean grade-point average (

GPA) was 2.96, and the standard deviation was 0.21. What is the margin of error, assuming a 70% confidence level, to the nearest hundredth
Mathematics
1 answer:
umka21 [38]3 years ago
4 0

Answer:

The margin of error is of 0.01.

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1 - 0.7}{2} = 0.15

Now, we have to find z in the Z-table as such z has a p-value of 1 - \alpha.

That is z with a pvalue of 1 - 0.15 = 0.85, so Z = 1.037.

The margin of error is of:

M = z\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

Standard deviation was 0.21.

This means that \sigma = 0.21

Sample of 450:

This means that n = 450

What is the margin of error, assuming a 70% confidence level, to the nearest hundredth?

M = z\frac{\sigma}{\sqrt{n}}

M = 1.037\frac{0.21}{\sqrt{450}}

M = 0.01

The margin of error is of 0.01.

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