Question

In a random sample of 200 engineers, 137 have a master's degree. what is the sample proportion, p-hat, of engineers who have master's degrees?

Answer 1

The sample proportion, p-hat, of engineers who have master's degrees is   68.5% out of 200 engineers.

p-hat proportion:

In this proportion,  "p" denotes the probability of a certain event occurring or a certain parameter being true for a certain population, but when a population is large, it may be impractical or impossible to measure it directly. So, we have used the proportion for that cases.

The general form for calculating p-hat proportion is,

$\hat{p}=\frac{x}{y}$

where

x  is the number of successes in the sample, and

y is the size of the sample.

Given,

In a random sample of 200 engineers, 137 have a master's degree.

Here we need to find the the sample proportion, p-hat, of engineers who have master's degrees

According to the question,

x = 137 (number of successes in the sample)

and y = 200 (size of the sample)

Now apply the value on the formula then we get,

$\hat{p}=\frac{137}{200}$

So, the value of p-hat is

$\hat{p}=0.685$

The results are usually reported as a percentage, which in this case would be

=> 0.685 x 100 = 68.5%

Therefore, the sample proportion, p-hat, of engineers who have master's degrees is 68.5% out of 200 engineers.

To know more about p-hat proportion here

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