Question

In a random sample of size 49, 29 people say they generally get less than 8 hours of sleep a night. Calculate the point estimates p^ and q^

Answer 1

Here, we have given that,

n = total number of people = 49

x= number of people who say generally they get less than 8 hours of sleep out of total 49 people=29

we know that the $\hat p$ and $\hat q$ best point estimate of the population.

Now, we want to find $\hat p$ and $\hat q$

$\hat p$=sample proportion = probability of success

=$\frac{ x} {n}$

=$\frac{29}{49}$

= 0.59

Now,

$\hat q$ = probability of failure

= $1- \hat p$

=1 - 0.59

= 0.41

Here, we get the

$\hat p$= 0.59 and $\hat q$ = 0.41