Question

A research company wants to know what will happen to the company's R&D spending in the next year. Questionnaires go to 940 companies and they submit the following responses: Higher (260); Lower (220); Same (210); and No Idea (250). Excluding the No Idea responses, are the other three options equally likely? Use alpha = 0.05.

Answer 1

Null Hypothesis H0: Proportion of reponses of Higher, Lower and Same options are equally likely.

Alternative Hypothesis Ha: At least one proportion of reponses of Higher, Lower and Same options are not equally likely.

We will use chi-square test of homogeneity for the hypothesis test.

If null hypothesis is true, Proportion of reponses of Higher, Lower and Same options are equal to 1/3

Total number of Higher, Lower and Same options responses = 260 + 220 + 210 = 690

Expected frequency for eah option = (690) * (1/3) = 230

Chi Square test statistic,

= (260 - 230)^2 / 230 + (220 - 230)^2 / 230 + (210 - 230)^2 / 230

= 6.087

Degree of freedom = Number of groups - 1 = 3 - 1 = 2

P-value = P( > 6.087) = 0.0477

Since, p-value is less than 0.05 significance level, we reject null hypothesis H0 and conclude that there is strong evidence that reponses of Higher, Lower and Same options are not equally likely.