Please respond to 1 of following two (2) bulleted items: •The vast majority of t

Question

Please respond to 1 of following two (2) bulleted items:

•The vast majority of the world uses a 95% confidence in building confidence intervals. Give your opinion on why 95% confidence is so commonplace. Justify your response.

Construct a hypothetical 95% confidence interval for a hypothetical case of your choosing. Use your own unique choice of mean, standard deviation, and sample size to calculate the confidence interval.

Select one (1) option provided below and analyze how it will influence your confidence interval:

•The confidence changes to 90%.

•The confidence changes to 99%.

•The sample size is cut in half.

•The sample size is doubled.

•The sample size is tripled.

Provide a rationale for your response.

Explanation / Answer

Why don't we use 99% confidence interval instead of 95% when 99% CI means more confidence in the mean lying between the interval that we arrive at, right? That is because as the confidence level increases, the interval goes wider and hence, the margin of error also increases (that's why the confidence increases). So a larger interval will increase your confidence but at the same time also increase the range of confidence, thus errors. For example, I am 99% confident that I will score between 40 and 90 in the exam OR I am 95% confident that I will score between 70 and 90 in the exam. The interval is too wide in the first statement.

Hypothetical Example - Sample size = 10 => degrees of freedom = n-1 = 9. Let mean = 250 pounds and SD = 25 pounds.

95% CI (two tailed test) = 240 +/- 2.262*25/root(10) = 222.117 < x < 257.883.

a,b) Confidence Level changed - As we increase the confidence level, the interval would widen and vice versa.

c,d,e) Change in sample size - We calculate standard error as standard deviation divided by square root of sample size. So, if we increase the sample size, the SE will reduce. In other words, if you increase the sample size it means you're taking more number of pulls from the population data and thus, your result will get closer to the population mean, the standard error decreases and the sampling distribution will become normal

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