An apple farmer has determined, based on historical data, that the average mass of apples grown from her orchard is 130 grams. She decides to test a new fertilizer that is advertised as being "packed with plant nutrients intended to increase average fruit mass".

(a) After applying the new fertilizer, the farmer collects a sample of 40 apples and ob- serves a sample mean of 124 grams and a sample standard deviation of 16 grams. Conduct a one-samplet-test of a mean testing the null hypothesis that the popula- tion mean is 130 grams against the alternative hypothesis that the population mean isgreaterthan 130 grams. In other words, conduct a one-sided hypothesis test in- vestigating whether the mass has increased as desired. Use a significance threshold of= 0.05. You may use geogebra to help out with computations for this problem.

(b) Using the same sample as in part a) (mean of 124 grams, standard deviation of 16 grams,n= 40) conduct a one-samplet-test of a mean testing the null hypothesis that the population mean is 130 grams against the alternative hypothesis that the population mean isnot equal to130 grams. Use a significance threshold of= 0.05. You may use geogebra to help out with computations for this problem.

(c) Do the tests you conducted in parts a) and b) tell a consistent story about the effect of the fertilizer? With the goal of determining whether switching to this new fertilizer would be an effective strategy for increasing apple mass, interpret the findings from these two tests. Taking the results from both tests together, would you conclude that the switch to the new fertilizer would be helpful, harmful, or neither? Justify your answer.