Question

The table below lists the observed frequencies for all four categories for an experiment.

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Category 1 2 3 4

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Observed Frequency 12 14 18 16

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The null hypothesis for the goodness-of-fit test is that the proportion of all elements of the population that belong to each of the four categories is the same. What is the expected frequency for the second category?

The null hypothesis for the goodness-of-fit test is that the proportion of all elements of the population that belong to each of the four categories is the same. The expected frequencies for the four categories are:

Category 1:

Category 2:

Category 3:

Category 4:

The null hypothesis for the goodness-of-fit test is that the proportion of all elements of the population that belong to each of the four categories is the same. What are the degrees of freedom for this test?

The null hypothesis for the goodness-of-fit test is that the proportion of all elements of the population that belong to each of the four categories is the same. The significance level is 1%. What is the critical value of chi-square? 12.838 13.277 14.860 11.345

The null hypothesis for the goodness-of-fit test is that the proportion of all elements of the population that belong to each of the four categories is the same. What is the value of the test statistic, rounded to three decimal places?

Answer 1

ANSWER::

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency(p)	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
1	0.250	12.000	15.000	-0.77	0.600
2	0.250	14.000	15.000	-0.26	0.067
3	0.250	18.000	15.000	0.77	0.600
4	0.250	16.000	15.000	0.26	0.067
total	1.000	60	60		1.3333
test statistic X2 =	1.333