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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