A headline in a ce in newspaper states hat most stay at rst job less than 2 year

Question

A headline in a ce in newspaper states hat most stay at rst job less than 2 years. That headline is based on an online poll of 280 college graduates. Among those polled, 75% stayed at their first full-time job less than 2 years. Complete parts (a) through (d). a. Assuming that 5 % e rue percentage o gra uates who stay a their first ob less than two years find he mean and standard deviation o he numbers o such graduates in rando y selected groups of 80 graduates The mean is graduates (Simplify your answer.)

Explanation / Answer

a. The mean is 140 graduates.

= np

= (280)(0.50)

= 140

The standard deviation is 9.9 graduates.

= npq

= (280 x 0.50 x 0.50)

= 8.4

b)

The numbers of graduates among 280 who stay at their first job less than two years should usually fall between 123.2 and 214.8.

– 2 = 140 - 2 * 8.4 = 123.2

+ 2 = 140 + 2 * 8.4 = 156.8

c)

The actual number of surveyed graduates who stayed at their first job less than two years is 296.

280 x 75% = 210

Since the actual number is outside of the range of usual values found in part (b), it is unusual.

The result suggests that the headline is justified.

Because the actual number of surveyed graduates who stayed at their first job less than two years is larger than the maximum usual value under the assumption that 50% is the true percentage. Therefore, it is unlikely that the true percentage is 50% or less.

d) Since the sample of 280 respondents is a voluntary response sample, the results are very questionable.

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