Statistics- Sampling distribution

Statistics - Sampling Distribution

1 . a . The mean of the population is equal to the mean of the sampling distribution , so the mean exam score is 100 . The standard error is given by

where n is the sample size , N is the population size and ? is the standard deviation of the population . So the answer is

b . The mean of the population is 100 . The standard error is given by

c . The mean of the population is 100 . The standard error is given by

d . The mean score remains the same no matter

how many exams are sampled However , the standard error gets smaller in c than in a , which shows that the larger the sample which is taken the lower the standard error is likely to be . This therefore reflects the advantages of taking larger samples in gaining a more accurate representation of the true population

2 . To solve this the sampling distribution of the mean needs to be defined . As the sample size is greater than 40 , the Central Limit Theorem states that the sampling distribution will be normally distributed

We know the mean of the sampling distribution is 2750 given that this is equal to the mean of the population . The standard error can be calculated as below

We want to know the probability that the mean is more than 2800 . Using the normal distribution as follows

This gives the probability that the mean of the sample is greater than 2800 calories is 0 .572

3 . a . Again...