Question

I have been getting many incorrect answers recently, if you are unsure please do not attempt. All i ask is all parts answered and with shown or explained work. Thank you (:

The following data represent the math SAT scores for a random sample of seniors from three different high schools.

School A	School B	School C
488	445	618
592	370	525
537	382	651
470	423	647
539	523	543

Using α=0.05, perform a hypothesis test to determine if the math median SAT score differs among these three high schools.

Answer 1

Here we need to test "wether the math median SAT score differs among these three high schools"

Let's write null hypothesis ( H₀ ) and the alternative hypothesis( H_a )

H_a : At least one pair of means of two high schools is different.

Using excel :

step 1) First enter the data in excel column.

step 2) Click on Data >>>Data Analysis>>>Anova: Single Factor

Then click on OK

step 3) select all the data values in "Input range"

Here level of significance is given as 0.05, so Alpha : 0.05

then click on Output Range

Select any empty cell

Look the following image:

then click on OK so we get the following output

p-value = 0.0017

and F critical value =4.885294

Decision rule:

1) If p-value < level of significance (alpha) then we reject null hypothesis

2) If p-value > level of significance (alpha) then we fail to reject null hypothesis.

Here p value = 0.00177 < 0.05 so we used first rule.

That is we reject the null hypothesis

Conclusion: At 5% level of significance there are sufficient differences of at least one pair among the three high schools means.

So correct option is B