Question

There are 318 teachers at a college. Among a sample of 115 teachers from this college, 67 have doctorates. Based on this sample, estimate the population proportion of teachers at this college with doctorates.

Answer 1

Answer:
`(67)/(115)` or 0.5826

Explanation:

Given : The total number of teachers in at a college = 318

In sample of n= 115 teachers from this college, the number of teachers with doctorates : x=67

Then, the sample proportion of teachers at this college with doctorates

`=\hat{p}=(x)/(n)\\\\=(67)/(115)=0.582608695652\approx0.5826`

Since the sample proportion is the best estimate of the population proportion.

Therefore , the estimated the population proportion of teachers at this college with doctorates =
`\hat{p}=(67)/(115)\  or\ 0.5826`