1 Find the expected frequencies 2 FInd the critical values a

1) Find the expected frequencies

2) FInd the critical values and identify the rejection regions

3) Find the chi-square test statistic

4) Decide whether to reject or fail to reject

5) Interpret

At a=0.01, test the claim that the 200 test scores shown below are normally distributed.

76.5-85.5

85.5-94.5(frequencey at 4)

Here it is necessary to estimate µ and ² of the normal distribution by xbar and ^²

Now we have to find first class mid points.

mean class mid point = (lower limit + upper limit) / 2

mean = 13887 / 200 = 69.435

variance = [ fx² - (fx)² / n ] / n-1

sd = sqrt(variance)

variance = 69.503

sd = sqrt(69.503) = 8.337

Now by using z-score formual we have to calculate probabilities.

z = (x - mean) /sd

z = (x - 69.435) / 8.337

Now we have to calculate z-score for each x that isfor infinity,94.5,85.5,76.5,67.5,58.5 and 49.5

This we can done by using EXCEL.

Now we have to find between probability.

where Ei = n * probability.

where Ei are the expected frequencies.

The hypothesis for the test is,

H0 : normal distribution is appropriate.

H1 : normal distribution is not appropriate.

Now the test statistic for testing is,

² = (O - E)² / E

where O is observed frequency and

E is expected frequency.

test statistic = 2.2879

n = number of classes = 5

d.f. = n-1 = 5-1 = 4

critical value we can find by using EXCEL:

=chiinv(probability,d.f.)

probability = alpha = 0.01

critical value 13.2767

test statistic < critical value

accept H0 at 1% level of significance.

And conclude that normal distribution is appropriate.