Question

Suppose that in the population, exactly 41% of all adults make a wish when they blow out candles on a birthday cake. If we select many random samples of size n = 400 people from this population, we know the sample proportion who make a wish when blowing out candles on a birthday cake will vary from sample to sample. The sampling distribution of the sample proportion would be Normal in shape and would have a standard deviation equal to what value? 0.4100 O 0.0320 0 0.0246 0.0500 0.0006

Answer 1

We have;

p = 40% = 40/100 = 0.4

1 - p = 1 - 0.4 = 0.6

n = 400

The standard deviation of sample proportion $\hat{p}$ =  $\sqrt{\frac{p(1-p)}{n}}$

σ = $\sqrt{\frac{0.4(1-0.4)}{400}}$

σ = $\sqrt{\frac{0.4(0.6)}{400}}$

σ =$\sqrt{\frac{0.24}{400}}$

σ = $\sqrt{0.0006}$

σ = 0.024494

Answer: σ = 0.0246