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lianna [129]
3 years ago
15

Determine the sample size needed to construct a 99​% confidence interval to estimate the average GPA for the student population

at a college with a margin of error equal to 0.7. Assume the standard deviation of the GPA for the student population is 1.0. The sample size needed is nothing. ​(Round up to the nearest​ integer.)
Mathematics
1 answer:
Volgvan3 years ago
3 0

Answer: n = 14

Step-by-step explanation: margin of error = critical value × σ/√n

Where σ = population standard deviation = 1

n = sample size = ?

We are to construct a 99% confidence interval, hence the level of significance is 1%.

The critical value for 2 tailed test at 1% level of significance is gotten from a standard normal distribution table which is 2.58

Margin of error = 0.7

0.7 = 2.58×1/√n

0.7 = 2.58/√n

By cross multipying

0.7×√n = 2.58

By squaring both sides

0.7^2 × n = 2.58^2

0.49 × n = 6.6564

n = 6.6564/0.49

n = 14

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Complete question :

A 12-foot by 15-foot patio is increased by placing a stone border around the patio. The width of the border is the same all around the patio.The perimeter of the patio after it is expanded is 74 feet. The equation which represents x, the width of the border is 2[(12+2x)+15+2x)]=74. What is the width of the border?

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Step-by-step explanation:

Solving for X in the perimeter equation :

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Answer:

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