Question

A random sample of 201 newborn piglets contains 90 females (data collected by Alexa Hopping and Brett Troyer, 2011). Calculate a 90% confidence interval for the proportion of all newborn piglets that are female.

Answer 1

Here we have given that,

n=number of newborn piglets= 201

x: number of newborn piglets contains females = 90

Now, we estimate the sample proportion as

=sample proportion of newborn piglets contains females

=

p=population proportion of newborn piglets contains females

Now we want to find the 90% confidence interval for the population proportion of newborn piglets contains females p

The formula for CI is as follows,

Now, first, we can find Z-critical value

c=confidence level =0.90

=level of significance= 1-c=1-0.90=0.10

                             =

                          = 1.645 Using EXCEL software =ABS(NORMSINV(probability =0.05))

The 90% confidence interval is,

The 90% confidence interval for the population proportion of newborn piglets contains females​​​​​​​ p are (0.390, 0.506)

Conclusion:

Here we can say that we are 90% confident that the true proportion of the population proportion of newborn piglets contains females​​​​​​​ (p) will fall inside this interval.