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: $\dfrac{67}{115}$ or 0.5826

Step-by-step 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

$=\hat{p}=\dfrac{x}{n}\\\\=\dfrac{67}{115}=0.582608695652\approx0.5826$  

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 = $\hat{p}=\dfrac{67}{115}\ or\ 0.5826$