Question

1.       A sample of 100 expert public health researchers were surveyed and their opinion about the possibility of the CO-Vid 19 spiking in the fall was accessed.  They were asked to predict if the spike would be much higher than in the spring, about the same as in the spring,  a very small spike or no spike at all. Of the 100, 40 reported much higher than in the spring spike, 30 reported about the same as in the spring, 20 a very small spike and 10 no spike at all.  The researcher wanted to know if these obtained results deviated significantly from what would be expected if there were no differences among the expectancies.

a.       State the null and alternative hypotheses

b.       Perform chi-square goodness of fit test

c.       What is the critical value of chi-square for this test

d.       What is your decision with respect to the null hypothesise.       Do these results deviate significantly from what would be expected by chance?  Describe this deviation

Answer 1

a)

Hypothesis:

Null Hypothesis Ho: There is NO significant difference between the observed and the expected value.

Alternative Hypothesis Ha: There is a significant difference between the observed and the expected value.

b)

Chi-square test of goodness of fit : The formula is given beolw;

As per below calculation table , we get Chi-square statistic value = 20 .......(1)

	Predict the spike in the spring
	High	Same	Very small	No	Total
Observed (O)	40	30	20	10	100
Expected (E)	25	25	25	25	100
(O-E)^2	225	25	25	225
(O-E)^2 / E	9	1	1	9	20

c)

Chi-square critical value for degrees of freedom (df) [ 4-1=3 ] and alpha(0.05) = 7.815 .....(2)

( Refer below Chi-square table)

d)

From the above (1) and (2) ; we get;

Since Chi-square statistic value = 20 > Chi-square critical value=7.815

Decision : Reject Ho

Conclusion : The obtained results deviated significantly from what would be expected if there were no differences among the expectancies.

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