In a maze running study, a rat is run in a T maze and the result of each run recorded. A reward in the form of food is always placed at the right exit. If learning is taking place, the rat will choose the right exit more often than the left. If no learning is taking place, the rat should randomly choose either exit. Suppose that the rat is given n : 100 runs in the maze and that he chooses the rig ht exit x : 62 times. Would you conclude that learning is taking place? (Use a : 0.01.) State the null and alternative hypotheses. O H0: [1 0.5 O H0: [1 : 0.62 versus Ha: p i O 62 O H0: [1 : 0.5 versus HE: D 0.5 O H0: [1 i 0.62 versus Ha: p : O 62 O H0: [1 : 0.5 versus HE: D > 0.5 Find the test statistic and the p-value. (Round your test statistic to two decimal places and your p-vaiue to tour decimal places.) State your conclusion. 0 The pavalue is less than alpha, so H0 is rejected. There is sufficient evidence to indicate that learning is taking place. 0 The p-value is less than alpha, so H0 is rejected. There is insufcient evidence to indicate that learning is taking place. 0 The p-yaiue is greater than alpha, so H0 is not rejected. There is insutficrent evidence to indicate that learning is taking place 0 The p-yaiue is greater than alpha, so H0 is not rejected. There is sufficient evidence to indicate that learning is taking place. You may need to use the appropriate appendix table or technology to answer this question. A production plant has two extremely complex fabricating systems; one system is twice as old as the other. Both systems are checked, lubricated, and maintained once every 2 weeks. The number of finished products fabricated daily by each of the systems is recorded for 30 working days. The results are given in the table. Do these data present sufficient evidence to conclude that the variability in daily production warrants increased maintenance of the older fabricating system? Use the p-value approach. (Use a = 0.05. Round your answer to two decimal places.) New System Old System x = 249 x = 240 S = 15.8 S = 28.4 1-2. Null and alternative hypotheses: O Ho: 012 022 O Ho: 012 = 022 versus Ha: 012 # 022 O Ho: 012 # 022 versus Ha: 012 = 022 O Ho: 012 = 022 versus Ha: 012 022 3. Test statistic: F = 4. p-value: O p-value 0.100 5. Conclusion: O Ho is not rejected. There is insufficient evidence to conclude that the variability warrants increased maintenance of the older system. O Ho is rejected. There is insufficient evidence to conclude that the variability warrants increased maintenance of the older system. O Ho is rejected. There is sufficient evidence to conclude that the variability warrants increased maintenance of the older system. O Ho is not rejected. There is sufficient evidence to conclude that the variability warrants increased maintenance of the older system.To test the effect of alcohol in increasing the reaction time to respond to a given stimulus, the reaction times of seven people were measured. After consuming 89 ml of 40% alcohol, the reaction time for each of the seven people was measured again. Do the following data indicate that the mean reaction time after consuming alcohol was greater than the mean reaction time before consuming alcohol? Use a = 0.05. (Use Abefore - Mafter = Ad. Round your answers to three decimal places.) Person 1 2 3 4 5 6 7 Before 4 5 4 3 6 After 7 3 5 5 4 4 1-2. Null and alternative hypotheses: O Ho: Mg 0 O Ho: My = 0 versus /d # 0 O Ho: Mg # 0 versus ud = 0 O Ho: Hd = 0 versus My 0 3. Test statistic: t = 4. Rejection region: If the test is one-tailed, enter NONE for the unused region. t> 5. Conclusion: O Ho is rejected. There is sufficient evidence to indicate that the mean reaction time is greater after consuming alcohol. O Ho is not rejected. There is insufficient evidence to indicate that the mean reaction time is greater after consuming alcohol. O Ho is rejected. There is insufficient evidence to indicate that the mean reaction time is greater after consuming alcohol. O Ho is not rejected. There is sufficient evidence to indicate that the mean reaction time is greater after consuming alcohol.A producer of machine parts claimed that the diameters of the connector rods produced by its plant had a variance of at most 0.173 cm. A random sample of 19 connector rods from the plant produced a sample mean and variance of 1.3 cm and 0.58 cm, respectively. (a) Is there sufficient evidence to reject the producer's claim at the a = 0.05 level of significance? (Round your answers to three decimal places.) 1-2. Null and alternative hypotheses: O Ho: 02 = 0.173 versus Ha: 02 > 0.173 O Ho: 02 = 0.173 versus Ha: 02 0.173 versus Ha: 02 x 2