Question

In 2017, the mean age at first birth among US women living in metro counties was 27.7. Would you be more likely (or equally likely) to get a sample mean of 25 years if you randomly sampled 25 women or if you randomly sampled 50 women? Explain

. A population has a mean of 150 and a standard deviation of 16. a) What are the mean and standard deviation of the sampling distribution of the mean for N=25? b) What are the mean and standard deviation of the sampling distribution of the mean for N=50?

3. Given a test that is normally distributed with a mean of 100 and a standard deviation of 15, find: a) The probability that a sample of 73 scores will have a mean greater than 107. b) The probability that the mean of sample of 13 scores will be either less than 91 or greater than 10

Answer 1

In 2017, the mean age at first birth among US women living in metro counties was 27.7. Would you be more likely (or equally likely) to get a sample mean of 25 years if you randomly sampled 25 women or if you randomly sampled 50 women? Explain .

Answer: As sample size increases we get more likely or approximate result so we sampled 50 women. to get more correct results.

Que.2

A population has a mean of 150 and a standard deviation of 16.

a) What are the mean and standard deviation of the sampling distribution of the mean for N=25?

b) What are the mean and standard deviation of the sampling distribution of the mean for N=50?

Using sampling distribution when distribution is not known and mean , standard deviation and sample size is given then

Mean would not be change it still remains same and standard deviation will be sd / sqrt (n) .

Part a.

Mean =    150

Part b.

Mean =    150

3. Given a test that is normally distributed with a mean of 100 and a standard deviation of 15, find: a) The probability that a sample of 73 scores will have a mean greater than 107. b) The probability that the mean of sample of 13 scores will be either less than 91 or greater than 10

Answer :

Part a.

n= sample size = 73

( Using excel we have command to find probability   =NORMSDIST(3.9872) = 0.99997 )

Probability above 107 is 0.00003

Part b .

P(x < 91 or x > 10 ) = P( x < 91) +P(x >10)

n = 13

Probability below 91 and above 100 is 0.51526