Question

On each trial of a digit span memory task, the participant is asked to read aloud a string of random digits. The participant must then repeat the digits in the correct order. If the participant is successful, the length of the next string is increased by one. For instance, if the participant repeats four digits successfully, he will hear five random digits on the next trial. The participant's score is the longest string of digits he can successfully repeat.
A professor of cognitive psychology is interested in the number of digits successfully repeated on the digit span task among college students. She measures the number of digits successfully repeated for 49 randomly selected students. The professor knows that the distribution of scores is normal, but she does not know that the true average number of digits successfully repeated on the digit span task among college students is 7.06 digits with a standard deviation of 1.63 digits.

a. The expected value of the mean of the 49 randomly selected students, M, is:_____
b. The standard error of M is:______

Answer 1

Answer:

a) The expected value of the mean of the 49 randomly selected students, M, is 7.06 digits

b)

The Standard error of the mean is 0.2328

Step-by-step explanation:

Explanation:-

Given sample size 'n' = 49

The Expected value of the mean of 49 randomly selected students

μₓ = μ =7.06 digits  

b)

The Standard error of the mean determined by

$S.E = \frac{S.D}{\sqrt{n} }$

Given sample size 'n' = 49

The Standard deviation 'σ' = 1.63 digits

The Standard error

$S.E = \frac{S.D}{\sqrt{n} }$

$S.E = \frac{1.63}{\sqrt{49} } = 0.2328$

Final answer:-

a) The expected value of the mean of the 49 randomly selected students, M, is 7.06 digits

b) The Standard error of the mean is 0.2328