Question

# Suppose there is a random sample of 1,196 observations, divided into four groups. The table below...

Suppose there is a random sample of 1,196 observations, divided into four groups. The table below summarizes the count of observations that were seen in each group.

 Group 1 Group 2 Group 3 Group 4 574 215 120 287

We are interested in testing the null hypothesis H0:p1=0.5,p2=0.2,p3=0.1,p4=0.2.

a) What is the appropriate alternative hypothesis?

 HA:All of the proportions are incorrect. HA:At least one of the proportions is incorrect. HA: All of the proportions are equal to each other.

b) What is the value of the test statistic?

Round your response to at least 3 decimal places.

c) The p-value falls within which one of the following ranges:

 p-value > 0.10 0.05 < p-value < 0.10 0.025 < p-value < 0.05 0.01 < p-value < 0.025 p-value < 0.01

d) What conclusion can be made at the 5% level of significance?

 There is very strong evidence against the null hypothesis, and therefore it is rejected in favour of the alternative hypothesis. There is no significant evidence against the null hypothesis, and therefore the null hypothesis is not rejected.

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