The heights of male college students in a particular random sample are given (in
ID: 3180061 • Letter: T
Question
The heights of male college students in a particular random sample are given (in inches). It is known that the standard deviation of heights for all college age males in the US is 3 inches. Construct a 90% confidence interval for the mean heights of college age males in the US. Show all steps. Which part of your calculations are the maximum error(s)? How might your mane maximum error(s) smaller? On a standardized test that results in normally distributed scores, the mean score for public school students is 72. A random sample of 36 students in a charter school achieve a mean score of 75, and their scores have a standard deviation of 4.5. Using this evidence, can we say that charter school students do better on this standardized test than public school students? Give your null and alternative hypotheses, show your calculations, and explain your answer.Explanation / Answer
1)
Calculate confidence interval for the population mean, with the formula:
x ± z* / (n)
n = 20, = 3, x = 63.5
Subtract the confidence level (Given as 90 percent in the question) from 1
and then divide the result by two. This is your alpha level, which represents
the area in one tail.
(1 – .90) / 2 = .05
Subtract your result from Step 1 from 1 and then look that area up in the
z-table to get the z-score:
Plug the numbers into the second part of the formula and solve:
z * / (n)
= 1.644854 * 3/(20)
= 1.103402
For the lower end of the range,
63.5 – 1.103402 = 62.397
For the upper end of the range
63.5 + 1.103402 = 64.603
90% ci is (62.397, 64.603)
b) z* / (n) is the maximum error. For a 90% CI, z is standard and is as given. Both cannot be changed or will not vary. The only parameter that can be varied is the sample size n. Observe from the formula, as 'n' increases the overall maximum error value reduces.
Therefore increasing sample size can provide a smaller CI range.
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