related to Calculus

Question

A school principal claims that the students in his school are above average intelligence. A random sample of 30 students IQ scores has a mean score of 112.5. The mean population IQ is 100 with an SD of 15. Is there sufficient evidence to support the principal’s claim?

solve using integration.

Given CI is 95% and An area of .05 is qeual to 1.645 of z-score.

Answer 1

Hi Bicf,

This is more related to statistics rather than calculus.

In hypothesis testing, the null hypothesis must contain an equal sign. It was given that the principal thought the average scores (intelligence) were greater than the population mean. So the alternative hypothesis would be H_a>100. Hence the null hypothesis is H_o<=100.

Since we know the population standard deviation and the sample size is at least 30 (Central Limit Theorem) we can use the z-statistic

Z_statistic=(sample mean-population mean)/(pop std dev/sqrt(sample size))

In this case, (112.5-100)/(15/sqrt(30)) which is around 4.56.

Because 4.56 falls greater than the critical z-value of 1.645, reject the null hypothesis, H_o.

So, there is enough evidence to support the principal's claim.

I hope this helps!