A group of 62 randomly selected students have a mean score of 28.3 on a standardized placement test. The population SD for all students taking the test is $σ = 3.4$ $sigma = 3.4$ . What is the 90 percent confidence interval for the mean score?

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A group of 62 randomly selected students have a mean score of 28.3 on a standardized placement test. The population SD for all students taking the test is $σ = 3.4$ $sigma = 3.4$ . What is the 90 percent confidence interval for the mean score?

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Answer 1 · 2016-07-13T10:15:49

Population mean is likely to fall between $29.005$ $29.005$ and $27.595$ $27.595$

Explanation:

Given -

$¯ x = 28.3$ $barx=28.3$
$n = 62$ $n=62$
$σ = 3.4$ $sigma=3.4$
$z$ $z$ score for 90% confidence interval $1.64$ $1.64$
$S E = \frac{σ}{\sqrt{n}} = \frac{3.4}{\sqrt{62}} = \frac{3.4}{7.87} = 0.43$ $SE=sigma/sqrtn=3.4/sqrt62=3.4/7.87=0.43$

90% confidence interval is defined by the formula

$μ = ¯ x + (S E \times z)$ $mu=barx+(SExxz)$ --------upper limit
$μ = 28.3 + (0.43 \times 1.64) = 28.3 + 0.705 = 29.005$ $mu=28.3+(0.43 xx 1.64)=28.3+0.705=29.005$

$μ = ¯ x - (S E \times z)$ $mu=barx-(SExxz)$ --------Lower limit
$μ = 28.3 - (0.43 \times 1.64) = 28.3 - 0.705 = 27.595$ $mu=28.3-(0.43 xx 1.64)=28.3-0.705=27.595$

Look at the diagram

Sample means are normally distributed around the population mean $μ$ $mu$

An interval is developed as $29.005$ $29.005$ and $27.595$ $27.595$ . There is 90% chance for the population mean to fall in this interval.

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A group of 62 randomly selected students have a mean score of 28.3 on a standardized placement test. The population SD for all students taking the test is $σ = 3.4$ $sigma = 3.4$ . What is the 90 percent confidence interval for the mean score?

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

A group of 62 randomly selected students have a mean score of 28.3 on a standardized placement test. The population SD for all students taking the test is σ=3.4sigma = 3.4. What is the 90 percent confidence interval for the mean score?

1 Answer

Explanation:

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A group of 62 randomly selected students have a mean score of 28.3 on a standardized placement test. The population SD for all students taking the test is $σ = 3.4$ $sigma = 3.4$ . What is the 90 percent confidence interval for the mean score?