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lord [1]
3 years ago
14

Suppose that scores on the mathematics part of a test for eighth-grade students follow a Normal distribution with standard devia

tion σ = 150. You want to estimate the mean score within ±20 with 90% confidence. How large an SRS of scores must you choose? (Round your answer up to the next whole number.)
Mathematics
1 answer:
riadik2000 [5.3K]3 years ago
8 0

Answer:

We need an SRS of scores of at least 153.

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{1-0.9}{2} = 0.05

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.05 = 0.95, so z = 1.645

Now, find M as such

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

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

How large an SRS of scores must you choose?

This is at least n, in which n is found when M = 20, \sigma = 150. So

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

20 = 1.645*\frac{150}{\sqrt{n}}

20\sqrt{n} = 1.645*150

\sqrt{n} = \frac{1.645*150}{20}

\sqrt{n} = 12.3375

(\sqrt{n})^{2} = (12.3375)^{2}

n = 152.2

Rounding to the next whole number, 153

We need an SRS of scores of at least 153.

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