Week 4 assignment

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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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Maximum Upper Bound= 81.841207 Minimum Lower Bound= 29.073282 Maximum Upper Bound= 88.380938

Minimum Lower Bound= 44.17638 Maximum Upper Bound= 60.465064 1. What is the proportion of the 95% confidence intervals that contain 50 when n=10? When n=50? N=10: Minimum lower bound- 35.940688, Maximum upper bound- 80.065385 N=5-: Minimum lower bound- 44.444372, Maximum upper bound- 60.267119 2. What is the proportion of the 99% confidence intervals that contain 50 when n=10? When n=50? N=10: Minimum lower bound- 21.812057, Maximum upper bound- 100.888 N=50: Minimum lower bound- 42.813358, Maximum upper bound- 60.82404 3. How does the typical width of the confidence interval change when the confidence level increases? As with the previous one, confidence level increases, typical width of the confidence level also increases. This means that the interval needs to be wider to capture the true mean with higher certainty.

4. How does the typical width of the confidence interval change as the sample size increases? With sample size increases, typical width of the confidence interval decreases. Larger sample sizes provide more information which helps in reducing the uncertainty with the estimation of true mean. 5. What was one obvious difference when comparing your conference intervals when sampling from a Normal Distribution vs. a Skewed Distribution? What was consistent (similar) when increasing the sample size for both Normal and Skewed Distributions? The obvious difference is shown in the shape of the intervals. Within the normal distribution, these intervals seem to have a more symmetric and bell-shaped appearance. Within the skewed distribution, the intervals are asymmetric and skewed. This is expected when comparing both normal and skewed with how the shape is represented. With the increase in the sample size for both normal and skewed, width is seen to decrease. We can see with increases, the estimates become more accurate and less varying which gives the result of the narrow intervals. Effects of the increasing on the reduction of the width seems to apply to both normal and skewed. This allows the data to be more precise when estimating the true mean.

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