For each of the following scenarios, state the null hypothesis and identify the best statistical test to use to answer the question stated. (Don’t try to answer the specific question.)

a. Do stickleback fish occur with equal probability through all areas of a pond?

b. A large number of Douglas-fir and Western hemlock trees were sampled, and the presence or absence of pine beetles on each tree was recorded. Do the tree species differ in pine beetle occurrence?

c. A small number of Douglas-fir and Western hemlock trees were sampled, and the presence or absence of pine beetles was recorded. Do the species differ in occurrence of pine beetles? The expected number of infested fir trees is calculated as 2.3.

d. Do patients change in mean body mass during a hospital stay? 

e. Does the amount of rainfall per day in a rainforest have a normal distribution?

f. Which sex weighs more on average in bald eagles: males or females? Assume that the distribution of body weight in each sex is normally distributed, but that the two sexes have markedly different variances.

g. Which sex travels more per day, on average, in sperm whales: males or females? Assume that the distribution of distance traveled is very different from a normal distribution in each sex (but similar between sexes) and that sample size is small.

h. Do cats have greater strength in their dominant front paw (usually the right) than in their other front paw (usually the left)? The data are measurements of strength in dominant paw and other paw of a random sample of cats.

i. Does the mean number of chirps per minute by male crickets differ when the same crickets are measured at 15^°C and at 25^°C?

j. The data are water samples taken at the local beach. Does the mean number of bacteria per milliliter differ from 130 individuals per 100 ml?