For a particular population, a sample of n = 4 scores has an expected value of 10. For the same population, a sample of n = 25 scores would have an expected value of ____.
a. 4
b. 8
c. 10
d. 20
your expected value should not change, just your variance around the mean.
It will stay 10.
To find the expected value for a sample of n = 25 scores, we can use the property that the expected value is a population parameter and it remains the same regardless of the sample size.
Since the expected value for the population is 10, the expected value for the sample of n = 25 scores would also be 10.
Therefore, the correct answer is c. 10.
To determine the expected value for a sample size of 25 scores, we can use the concept of the law of large numbers. According to this law, as the sample size increases, the sample mean gets closer to the population mean.
In this case, we know that the expected value for a sample of 4 scores is 10. This means that on average, the scores in a sample of 4 will add up to 10.
Since the concept of the law of large numbers applies, we can expect that the larger sample of 25 scores will also have an expected value that is closer to the population mean. Therefore, we can conclude that the expected value for a sample of 25 scores would also be 10.
So, the correct answer is c. 10.