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You measure 48 textbooks' weights and find they have a mean weight of 49 ounces. Assume the...

Question:

You measure 48 textbooks' weights and find they have a mean weight of 49 ounces. Assume the population standard deviation is 10.7 ounces.

Construct a 95% confidence interval for the true population mean textbook weight. Use z = 2 for the calculations.

Confidence Interval:

Confidence interval gives range of all possible values likely to be true population mean at given level of confidence. The width of the confidence interval is determined by margin of error.

Answer and Explanation:

Given that;

{eq}n=48\\\bar X=49\\\sigma=10.7 {/eq}

Use equation below to construct 95% confidence interval for population mean:

{eq}\displaystyle \left(\bar X\pm Z_{\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}}\right) {/eq}

The critical value z that correspond to 95% level of confidence is equal to 1.96:

{eq}\displaystyle \left(49\pm 1.96\times \frac{10.7}{\sqrt{48}}\right)\\(49\pm 3.03)\\(45.97, 52.03) {/eq}


Learn more about this topic:

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Finding Confidence Intervals with the Normal Distribution

from Statistics 101: Principles of Statistics

Chapter 9 / Lesson 3
14K

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