Suppose the true population proportion werep= 0.5 and a researcher takes asimple random sample of sizen= 50.
(a) find and interpret the standard deviation of the sample proportion ˆp.
(b) calculate the probability that the sample proportion will be larger than 0.55 for a random sample ofsize 50.

answer is almost 0 i.e impossible event.

Step-by-step explanation:

given that the  the true population proportion were

p= 0.5

a) Std deviation of sample proportion =

This is the std deviation for a single trial.  We know in binomial variance is npq.  Using this we can say for a single trial, variance would be pq/n and hence std deviation of proportion is square root of pq/n

b) The probability that the sample proportion will be larger than 0.55 for a random sample ofsize 50

= P(p>0.55)

=

.19875994384

step-by-step explanation:

1699/ 8548

14.3

step-by-step explanation:

add all the numbers together.

9 + 12 + 15 + 16 + 17 + 17 = 86

now, divide 86 by how many numbers we have: 6.

86 / 6 = 14.3