Week 4 assignment

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National University College *

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100

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Economics

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Jan 9, 2024

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docx

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6

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Normal Distribution Minimum Lower Bounds= 30.82692 Maximum Upper Bounds= 69.201075 Minimum Lower Bounds= 26.248631 Maximum Upper Bounds= 71.414959
Minimum Lower Bounds= 43.109353 Maximum Upper Bounds= 57.21103 Minimum Lower Bounds= 41.43613 Maximum Upper Bounds= 58.880671 1. What is the proportion of the 95% confidence intervals that contain 50 when n=10? When n=50? N=10: Minimum Lower bound= 28.946322, Maximum Upper bound= 67.141994
N=50: Minimum Lower Bound= 43.030793, Maximum upper bound= 56.879564 2. What is the proportion of the 99% confidence intervals that contain 50 when n=10? When n=50? N=10: Minimum lower bound- 26.950715, Maximum upper bound- 73.936448 N=50: Minimum lower bound- 41.730853, Maximum upper bound- 58.579219 3. How does the typical width of the confidence interval change when the confidence level increases? When going from 95% to 99%, we can see the confidence level increase because the width of the interval also increases. Higher confidence level shows the needs to be wider in order to capture the true mean with more certainty. 4. How does the typical width of the confidence interval change as the sample size increases? With the increase in the sample size, the typical width of the confidence level decreases. With larger sample sizes we are given more information which does reduce uncertainty with estimation that the true mean. Narrower intervals are possible when more data is available. Right Skewed Distribution Minimum Lower Bound= 36.927789
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