Question

1. Given a proportion problem where the population proportion π=0.15 and sample size n=50. What is the sampling distribution of the sample proportion?

2. given a proportion problem where the population proportion π=0.1 and sample size n=40. What is the sampling distribution of the sample proportion?

3. If you take a sample of size n from a distribution that is not normal where the mean and standart deviation are given on the bottom. what is the sampling distribution of the sample mean?   µ=12 , σ=3 , n= 16

Answer 1

Solution :

1)

Given that,

= 0.15

1 - = 1 - 0.15 = 0.85

n = 50

The sampling distribution of the sample proportion

= ( * (1 - )) / n = (0.15 * 0.85)) / 50 = 0.0505

2)

Given that,

= 0.1

1 - = 1 - 0.1 = 0.9

n = 40

The sampling distribution of the sample proportion

= ( * (1 - )) / n = (0.1 * 0.9)) / 40 = 0.0474

3)

Solution :

Given that,

mean = = 12

standard deviation = = 3

n = 16

The sampling distribution of mean and standard deviation is ,

= 12 and

= / n = 3 / 16 = 3 / 4 = 0.75