SOLUTION: The average score in the entrance examination in Mathematics at CBN High School is 80 with a standard deviation of 10.A random sample of 40 students was taken from these year's exa

Question 1061944: The average score in the entrance examination in Mathematics at CBN High School is 80 with a standard deviation of 10.A random sample of 40 students was taken from these year's examinees and it was found to have a mean score of 84.Does this indicates that this year's batch is better than the previous batches?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
The problem has to state a significance level, usually if the significance level is not stated we choose 5%
:
Ho: x = 80
Ha: x > 80
:
This is a one-tailed test and we can use Normal distribution z-values since the sample size > 30 and the population is very large compared to sample
:
standard error = 10 / square root(40) = 1.5811
:
z-value test statistic = (84-80) / 1.5811 = 2.5299 approximately 2.53
:
At a 5% significance level, the critical value for a one tailed test is found from the table of z-scores to be 1.645. Since the test statistic is > critical value, we reject the null hypothesis.
:
***************************************************************
This means either a rare event has occurred or this years batch
is better than previous batches'
***************************************************************
:

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