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Viefleur [7K]
3 years ago
13

A simple random sample of 125 SAT scores has a mean of 1522. Assume that SAT scores have a population standard deviation of 335.

Construct a 95% confidence interval estimate of the mean SAT score and then correctly interpret your interval.
Mathematics
1 answer:
Fed [463]3 years ago
7 0

Answer:

1463.3\:

Step-by-step explanation:

Since the population standard deviation \sigma, is known, we use the z confidence interval for the mean.

This is given by:

\bar X-z_{\frac{\alpha}{2} }(\frac{\sigma}{\sqrt{n} } )\:

For a 95% confidence interval we use z=1.96.

It was also given that: n=125, \bar X=1522 and \sigma=335

Let us substitute the values to get:

1522-1.96(\frac{335}{\sqrt{125} } )\:

1463.3\:

<u>Interpretation:</u>

We can say with 95% confidence that the interval between 1463.3 and 1580.7 SAT scores contains the population mean based on the sample 125 SAT scores.

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