## Question 511:

1## Answer:

No answer provided yet.We will want to construct a 95% confidence interval around the sample proportion of nails less than 3 inches. The proportion is 25/100 = .25, which is denoted p.

- We need to construct the standard error of the mean (SEM), which is made up of the standard deviation divided by the square root of the sample size. For a proportion the standard deviation is the square root of p times 1-p = .25*.75 = SQRT(.1875) = .433.
- We divide the standard deviation by the squre root of the sample size = .433/SQRT(100) = .043 to get the SEM.
- Next we find the margin of error which is the SEM times the critical value from the normal distribution (z-score) for 95% of the area. We can look this up using the percentile to z-score calculator . We select (1-sided) since we're interested in only the proportion of nails shorter than 3 inches. We get 1.64. This gets us a margin of error of 1.64*.043 = .071.
- The confidence interval is constructed by adding and subtracting the margin of error to the proportion. .25-.071 and .25+.071 = a 95% confidence interval between .179 and .321.
- So we'd interpret this as saying, we can be 95% confident the true percent of nails LESS than 3 inches is between 17.9% and 32.1%.