The mean NAT scores of Grade 10 students is 65. Sixty students where chosen and found that the standard deviation of their scores is 5. What is the probability that their mean is below 64?

Answer 1

10 stidents = n = sample size

sampe mean = 65 = xbar

standard deviation = 5 = s

what is probabiltiy population mean = mu = 64?

normal distribution is close, but sample size is too small, use a flatter t distribution and t tables,

assume alpha = .05 df = n-2 = 8, 2 tails, find the row with df and column with .05 2 tails

t calculated = (64-65)/s/sqrn= -1/5/sqr10 =- .632

corresponding area = .296 29.6% probability mu less than 64, 70.4% probability >64

population standard deviation = s/sqr(n) = 5/sqr10 = about 1.58

50% probability population mean is less than 65

Ho: pop mean = 65

Ha: pop mean = 64

fail to reject Ho, if t calc < t expected

if p>alpha