Question

Given that the heights of adult males show a mean of 69” and standard deviation 2.7.” A sample of 37 adult males shows a mean of 68.2” and standard deviation of 2.9.”

1.Which of the following shows mean of population , mean, standard deviation of a population and s in this order?

a. 69” 2.7” 68.2” 2.9”

b. 69” 68.2” 2.9” 2.7”

c. 69” 68.2” 2.7” 2.9”

d. 68.2” 69” 2.7” 2.9”

2. What is the standard deviation of the sample means of all simple random samples of size 37 from this population?

a) 2.7”

b) 2.9”

c) 0.44”

d) 0.07”

Answer 1

Given:-  

Mean of the populaiton ( ) = 69''

Standard Deviation of the population ( ) = 2.7''

Mean of the sample ( ) = 68.2''

Standard Deviation of the sample ( s ) = 2.9''

sample size ( n ) = 37

For part a) we need to arrange the given information as follows,

(mean of population , mean of the sample, standard deviation of a population and  standard deviation of the sample ) =  69”, 68.2”, 2.7”, 2.9”

Hence answer to the question is option C.

for part b)

Need to calculate standard deviation of the sample means.

we will denote the standard deviation of the sample means as  .

₌ / n = 2.7 / 37 = 0.44''

Answer to this question is option C,