Question

In a four-year psychedelic-mushroom experiment, 93 of the 300 subjects reported experiencing “strong or extreme fear” after using psychedelic mushrooms.

a)Find a point estimate (ˆp)for the percentage of all people who experience “strong or extreme fear” after using psychedelic mushrooms.

b)Find the 95% margin of error(E)for the estimate in (a).

c)Make and interpret a 95% confidence interval (ˆpE) for the percentage of all people who experience “strong or extreme fear” after using psychedelic mushrooms.

Answer 1

Solution :

Given that,

n = 300

x = 93

Point estimate = sample proportion = $\hat p$ = x / n = 93/300=0.31

1 - $\hat p$   = 1-0.31 =0.69

At 95% confidence level the z is ,

$\alpha$ = 1 - 95% = 1 - 0.95 = 0.05

$\alpha$ / 2 = 0.05 / 2 = 0.025

Z$\alpha$/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E = Z$\alpha$ / 2    * $\sqrt$ ((($\hat p$ * (1 - $\hat p$ )) / n)

= 1.96 ($\sqrt$((0.31*0.69) /300 )

= 0.0523

A 95% confidence interval for population proportion p is ,

$\hat p$ - E < p < $\hat p$ + E

0.31-0.0523 < p <0.31+ 0.0523

0.2577< p < 0.3623

The 95% confidence interval for the population proportion p is : 0.2577, 0.3623