Question

On a national test of “mental intensity,” mis 20 and the standard deviation 6.28. Students in your class produce the following scores:

25, 26, 34, 14, 33, 29, 22, 18, 16, 13, 21, 20, 22, 21, 34, 30

Using the criterion of 0.05 and both tails of the sampling distribution, determine if your class is representative of the population.

Answer 1

We will use a one-sample t-test to solve this question.

Null hypothesis: H₀: The average score of students on national test of mental intensity is 20.

Alternate hypothesis: H_a: The average score of students on national test of mental intensity is NOT equal to 20.

We have population mean = 20

sample mean = 23.625; sample standard deviation = 6.869 (This can be calculated using MS Excel formula STDEV.S()

sample size = 16; hence degrees of freedom = 16-1 = 15

test statistic =

5- 23.625 – 20 3.625 , 6.869 1.7173 = 2.111 V16

The critical t-value can be read off a standard t-table for significance level of 0.05 with 15 degrees of freedom to be 2.131

Since the calculated t value (2.111) <  critical t value, then we fail to reject the null hypothesis and conclude that the sample is representative of the population.