A manufacturer of pens and pencils has created a new, ergonomically designed, me

Question

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 "at least 80% of college students believe the new pencil is more comfortable"? Briefly explain. d. Based on the information in the sample, find the sample size needed to calculate a 99% confidence interval to within 2.5 percentage points of the true percentage.

Explanation / Answer

Using Minitab one sample proportion test:

Test and CI for One Proportion

Test of p = 0.8 vs p > 0.8

Exact
Sample X N Sample p 95% Lower Bound P-Value
1 287 350 0.820000 0.782806 0.193

Sample proportion = 287/350 = 0.82

Std error=SQRT( p(1-p)/n )= 0.0205

95% confidence interval

=(0.82-0.0402, 0.82+0.0402)

= (0.7797, 0.8602)

C)P-value 0.193 > alpha =0.05 we do not reject null hypothesis so we conclude that it is reasonable to claim atleast 80% collegestudents believe the new pencil is more comfortable

Hope this will helpful. Thanks.

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