Question

neu value for X05 and for X01 ? 3. A researcher wishes to determine whether four comnercilly available standardiood ble standardiz achievement tests differ in their popularity. He obtains a random samp distric achieve le of 60 school ts in his region of the country and asks each superintendent which standardized ment test is used. (Assume that each district uses such a test, and only four tests exist.) The researcher has no basis for hypothesizing which test, if any, is preferred by school districts. The results are as follows: Test A B CD Frequency of selection 18 6 12 24 (a) Give, in symbolic form, two equivalent statements of Ho for this situation. (b) Can H, be written in a single symbolic statement? (Explain.) (c) Compute the expected frequencies under Ho. (Do they sum to n?) (d) Compute χ2 and test Ho at α-01. (e) From this x2, what is your general conclusion? That is, do the four achievement tests appear to differ in popularity?

Answer 1

(a)

If all four tests are equivalent then they should have equal proprotion so hypotheses are:

Or we can say expected frequecies should be equal to observed frequencies so

$H_{0}:E_{i}=O_{i},i=1,2,3,4$

(b)

Here alternative hypothesis shows that at least one proproiton differ or at least one observed frequency is not equal to expected frequency.

(c)

Here we have n = 60

So expected frequency for each test is:

E = 60 /4 = 15

Yes there sum is equal to 60.

(d)

Following table shows the calculations:

O	E	(O-E)^2/E
18	15	0.6
6	15	5.4
12	15	0.6
24	15	5.4
Total		12

The test statistics is:

$\chi^{2}=\sum \left ( \frac{(O-E)^{2}}{E} \right )=12$

Degree of freedom: df=n-1=11

The p-value using excel function "=CHIDIST(12,3)" is 0.0074

Since p-value is less than 0.01 so we reject the null hypothesis.

(e)

Since we reject the null hypothesis so there is evidence to conclude that four achievement tests appear to differ in popularity.