Carry out the test. What is the pvalue given by the test? Based on this sample, what is the 95% confidence interval for the proportion of plants that will survive the herbicide in future experiments with large numbers of plants? Should the researchers' hypothesis be rejected? What is the minimum number of plants surviving out of 50 that would have given a non-significant result in this case? And what is the minimum number of plants surviving out of 50 that would have caused the researchers' hypothesis to be rejected because the number of plants surviving was too high? Problem 3. For this question we will use the hermit crab data that we used in the lab. We want to test whether there is a difference between hermit crabs fed on the fancy expensive pet shop mix ie 'hermitcrabmix' and crabs fed on home diets {home diets include both cornflakes and cornflakes plus vegiesl. We are interested in whether there are differences in terms of their weight or in terms of the amount they eat. What would be the best statistical test to use? Test whether there is a difference in weights between the crabs fed on the pet shop diet vs the ones fed on a home diet. What is the p-value given by the test? Do we conclude that there is a significant difference? Now test whether the crabs fed on the pet shop diet have a greater weight than the ones fed on a home diet. What is the pvalue given by the test? Do we conclude that there is a significant difference? Now test whether the crabs fed on the pet shop diet eat a different amount than the ones fed on a home diet. What is the pvalue given by the test? Do we conclude that there is a significant difference? How much, on average, do the crabs in the two groups eat? Problem 4. The data for this problem is in the 'variety trial data.x|sx' file available in LMS. An agronomist chooses 10 sites to trial two new varieties of wheat. At each site he chooses a single plot {same size at every site} and then divides it evenly into two. One side of each plot is randomly chosen for variety 1 and the other is used for variety 2. At the end of the season, each of the 20 subplots is harvested and the yield per hectare recorded in the 'variety trial dataxlsx' file. The agronomist wants to know whether there is a real difference in yield between the varieties. What would be the best statistical test to use? Carry out the test. What is the p-value given by the test? Can we conclude there a real difference in yield between the varieties? Based on the 95% confidence interval, what would we say is a