Question

Table 12.4 on page 486 showed the calculated sums of the observed frequencies, the expected frequencies, and their differences. Strictly speaking, those sums are not needed. However, they serve as a check for computational errors.

a) In general, what common value should the sum of the observer frequencies and the sum of the expected frequencies equal? Ex plain your answer.

b) Fill in the blank. The sum of the differences between each observed and expected frequency should equal

c) Suppose that you are conducting a chi-square goodness-of-fit test. If the sum of the expected frequencies does not equal the sample size, what do you conclude?

d) Suppose that you are conducting a chi-square goodness-of-fit test. If the sum of the expected frequencies equals the sample size, can you conclude that you made no error in calculating the expected frequencies? Explain your answer.

Short answer

Ans:

(a) The sum of the observed frequencies and the sum of the expected frequencies are equal when it has the common value of "n ".

(b) The sum of the difference between each sight and the expected frequency should be equal to zero.

Description:

If the required amount does not equal zero, there must be an error in the study.

(c) If the number of expected frequencies and the expected number of frequencies do not match the size of the sample, it can be concluded that there is an error in calculating the expected frequencies or in summarizing the expected frequencies and expected frequencies.

(d) There may be an opportunity to make more than two compensation errors in calculating expected frequencies.

Step-by-step solution

Step 1. Give information.

given,

Table 12.4 on page 486 showed the calculated sums of the observed frequencies, the expected frequencies, and their differences.

Step 2. (a)  The number of observed frequencies and the expected number of frequencies are equal if we have a standard value such as "n".

Description:

In Table 12.4, it is clear that $n=500$, the total number of observed frequencies is 500 and the total expected frequency is 500.

The expected amount of frequencies is equal to the sample size provided below:

$\begin{array}{r}\sum E_i=\sum n{p}_i\\ =n\sum p_i\\ =n\left(1\right)\\ =n\end{array}$

Hence, the sum of the observed frequencies and the sum of the expected frequencies are equal when it has the common value of "n ".

Step 3. (b)  Fill in the blanks.

The sum of the difference between each sight and the expected frequency should be equal to zero.

Description:

If the required amount does not equal zero, there must be an error in the study.

Step 4. (c)  Explanation:

From subsection (a), it is clear that the amount of observed frequencies and the total expected frequency equals the size of the sample.

If the number of expected frequencies and the expected number of frequencies does not match the size of the sample, it can be concluded that there is an error in calculating the expected frequencies or in summarizing the expected frequencies and expected frequencies.

Step 5. (d)  Now,

No, it is not possible to conclude that there is no error in calculating expected frequencies when the total required frequency equals the sample size.

Description:

There may be an opportunity to make more than two compensation errors in calculating expected frequencies.