A manufacturer of pens and pencils has created a new ergonom

A manufacturer of pens and pencils has created a new, ergonomically designed, mechanical pencil and plans to market it to college students. A random sample of 350 college students was selected and 287 said the new pencil felt more comfortable than other pencils.

(a) Calculate a 95% confidence interval for the proportion of college students who think
the new pencil is more comfortable.

(b) Interpret the interval above in terms of this problem.

(c)Is it reasonable (based on your interval above) to claim

Solution

Sample proportion = 287/350 = 0.82

Std error = rt of p(1-p)/n = 0.0205

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95% confidence interval we use z value for 95% -1.96 and +1.96

=(0.82-0.0402, 0.82+0.0402)

= (0.7797, 0.8602)

b) The meaning of this interval is that we are 95% confident that under normal conditions sample proportion will be between 0.7797 and 0.8602 and also predictor of population proportions.

c) As above 0.80 falls in this interval, it is reasonable to claim atleast 80% college
students believe the new pencil is more comfortable