## Question 511:

1

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.

1. 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.
2. We divide the standard deviation by the squre root of the sample size = .433/SQRT(100) = .043 to get the SEM.
3. 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.
4. 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.
5. 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%.

### Not what you were looking for or need help?

Ask a new Question

Browse All 869 Questions

Search All Questions: