List of top Mathematics and Quantitative Ecology Questions on Hypothesis testing asked in GATE EY

In a null hypothesis significance test, the significance level \(\alpha\) was set to 0.01. For which one or more of the following p values would the null hypothesis be rejected?

Students M and N sampled body lengths of two populations of a fish species using the same study design. The table below summarizes their data as mean \(\pm\) standard error.

Body length (cm)	Population I	Population II
Student M	\(8.0 \pm 1.2\)	\(6.2 \pm 0.7\)
Student N	\(10.0 \pm 0.6\)	\(5.1 \pm 0.3\)

Given that the data are normally distributed, when comparing the means of the populations using a t-test, which student will find a lower p-value?

All octopi dream every night, and sometimes change colour while dreaming. A student hypothesises that octopi change colour only when they dream about the food they ate that day. To test this hypothesis, the student conducts an experiment with two treatments that are randomly ordered, and separated by 2 days. In one treatment, she places 10 octopi in individual tanks in captivity and provides each one with a large crab to eat during the day. She then records the dream state colour of these octopi that night. Which one (or more) of the following would be an appropriate NEGATIVE control to test this hypothesis?