Kelsey randomly collected 100 UW female students\' height data. She calculated s
ID: 3231890 • Letter: K
Question
Kelsey randomly collected 100 UW female students' height data. She calculated sample mean (x) of her data and it is 165.0 cm (about 5.6 feet). She also calculated sample standard deviation (s) and it is 10.0 cm. g) What is the Critical Value when the level of confidence in 90%? h) What is the Margin of Error of the mean, when the level of confidence in 90%? i) What is the 90% Confidence Intervals of the Mean? j) Interpret the above answer. k) Obtaining a larger sample size will certainly cost more money and take more time. Despite this, why is a large sample size important? You already answered the first reason in a). When you achieve a large sample size, you do not have to worry about the shape of the original distribution to construct a confidence interval or conduct hypothesis testing because of CLT. Is there another reason? As you increase the sample size, what do you reduce? Show some math and explain.Explanation / Answer
(g) Critical value when level of confidence is 90%
here tcritical for dF = 100 -1 = 99 and alpha = 0.1 , two tailed
tcritical = 1.660
so Lower critical value of height = xbar - tcrit (s/ n) = 165 - 1.66 * ( 10/ 100) = 163.34
Upper critical value of height = xbar + tcrit (s/ n) = 165 + 1.66 * ( 10/ 100) = 166.66
(163.34, 166.64)
(h) Margin of the error of the mean = Critical value x Standard error of the statistic = 1.66 * (10/100) = 1.66
(i) 90% confidence interval for population mean = xbar +- t0.05,99 (s/ n)
= ((163.34, 166.64)
(j) We can interpret from the above answer that average height of UW female students have 95% probability to be in between 163.34 cm to 166.64 cm.
(k) First thing bigger sample size more randomness and more data which will prompts more central tendancy of data.
as confidence interval width is inversely proportion to square root value of sample size. so more sample will help us to decrease margin of error and will also help in decreasing the width of confidence interval that will increase the accuracy to tell the average or mean height of UW women.
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