18. A researcher wondered whether there was a relationship between the amount of time a cat spent with his/her owner and activity patterns. To test that, he did a survey among 200 cat owners, asked them about the amount of time that they spent with their cat and whether their cat was more active during the night or during the day. The results are summarized in the following table (please note that "solitude" stands for cats that spend a lot of time on their own, "balanced" stands for cats that spend some time alone and some time with their owner and "symbiotic" stands for cats that spend most of their time with their owners): solitude balanced symbiotic day 2 68 50 120 night 28 32 20 30 100 70 200 a. Complete the expected frequencies in the table below. You must submit your calculations [if you do not submit your calculation, you will lose points). (6 points) solitude | balanced symbiotic day 120 night 80 30 100 70 200 b. In a hypothesis test on these data, what would be the hypotheses? (there is no need to complete an entire hypothesis test, only to state the hypotheses, at this point). (2 points) c. Calculate the appropriate test statistic. You must submit your calculations ( if you do not submit your calculation, you will lose points). (5 points) d. If you used a=.05, would you conclude that there is a relationship between the amount of time a cat spends with the owner and activity patterns?' Explain your answer. (2 points) Another researcher decided to use the same data to test whether cats showed a preference among day-time activity and night-time activity (ignoring the data on the amount of time spent with the owner). e. Which test should be used to test these data? Explain your answer. (3 points) f. Based on the table of the observed frequencies above, what would be the observed frequency of cats who are more active during the day (in the second researcher's study)? (1 point)