Question

Refer to the accompanying data display that results from a sample of airport data speeds in Mbps. Complete parts​ (a) through​ (c) below.	TInterval
	​(13.046,22.15) x overbarxequals=17.598 Sxequals=16.01712719 nequals=50

a. Express the confidence interval in the format that uses the​ "less than" symbol. Given that the original listed data use one decimal​ place, round the confidence interval limits accordingly.

____Mbpsless than<muμless than<______ Mbps

​(Round to two decimal places as​ needed.)

b. Identify the best point estimate of

muμ and the margin of error.The point estimate of μ is ____ Mbps.

​(Round to two decimal places as​ needed.)

The margin of error is E equals=_____Mbps.

​(Round to two decimal places as​ needed.)

c. In constructing the confidence interval estimate of muμ​,why is it not necessary to confirm that the sample data appear to be from a population with a normal​ distribution?

A.

Because the sample standard deviation is​ known, the normal distribution can be used to construct the confidence interval.

B.

Because the sample is a random​ sample, the distribution of sample means can be treated as a normal distribution.

C.

Because the population standard deviation is​ known, the normal distribution can be used to construct the confidence interval.

D.

Because the sample size of 50 is greater than​ 30, the distribution of sample means can be treated as a normal distribution.

Click to select your answer(s).

Answer 1

A.

n = 50

= 17.6

s = 16

(All data rounded to one decimal place)

Confidence Interval: 13.05 < < 22.15

B.

Best Point estimate of = 17.60

Margin of Error, E = 22.147-17.60

= 4.547

~ 4.55

C.

Correct Option is D.

Because the sample size of 50 is greater than​ 30, the distribution of sample means can be treated as a normal distribution.

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