A simple random sample of 25 recent graduates from a particular collage gives a

Question

A simple random sample of 25 recent graduates from a particular collage gives a sample mean starting salary of $24,000 with sample standard deviation $3,000. (a) Give the 95% confidence interval. We did an almost identical (with different numbers) question in class on 3/8. (b) Without doing any calculations, would the 99% confidence interval be narrower or wider than the 95% confidence interval. (c) Suppose the sample size was 50 (instead of 25) and the sample mean and standard deviation were the same values. Without doing any calculations, would the 95% confidence interval with n = 50 be narrower or wider than the 95% confidence interval with n = 25?

Explanation / Answer

Part (a)

Confidence Interval:

X bar (-/+) E

X bar = 24000

E = tc * ( s / sqrt (n)) = tc * (3000/sqrt(25))

tc is the critical value we find from normal table for 24 degrees of freedom at 5% level of significance. We get critical t (tc) 2.064.

E = 2.064 * (3000/sqrt(25))

X bar (-/+) E

24000 (-/+) 1238.4

22761.6 and 25238.4

The 95% confidence interval is (22761.6 to 25238.4).

Part ( b)

If we change the level of confidence from 95% to 99% then the critical value will get increased the value of margin error will be higher. For higher margin error the confidence interval will be wider.

Answer: wider

Part ( c )

If sample size will get increased then the margin of error will get decreased. When the margin error will get decreased the confidence interval will be narrower.

Answer: narrower

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