An experiment was conducted to compare the densities (in ounces per cubic inch) of cakes prepared from two different cake mixes. Six cake pans were filled with batter A, and six were filled with batter B. Expecting a variation in oven temperature, the experimenter placed a pan filled with batter A and another with batter B side by side at six different locations in the oven. The six paired observations of densities are as follows. Location 2 3 4 Batter A 0.134 0.103 0.097 0.142 0.130 0.143 Batter B 0.130 0.121 0.113 0.153 0.136 0.164 A USE SALT (a) Do the data present sufficient evidence to indicate a ditference between the average densities of cakes prepared using the two types of batter? (Use a - 0.01. Use atter a-Peatter"e) State the null and alternative hypotheses. O Hạ: H -0 versus H,: >0 O Hạ: H0 versus H -0 O H: H-0 versus H <0 O Hg: P <0 versus H: >0 O Hạ: H -0 versus H: 0 State the test statistic. (Round your answer to three decimal places.) State the rejection region. (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.) t> State the condusion. OH is not rejected. There is insufficient evidence to condude that there is a difference between the average densities of cakes prepared using the two types of batter. O H, is rejected. There is insufficient evidence to condude that there is a difference between the average densities of cakes prepared using the two types of batter. OH, is rejected. There is sufficient evidence to conclude that there is a difference between the average densities of cakes prepared using the two types of batter. O H, is not rejected. There is sufficient evidence to condude that there is a difference between the average densities of cakes prepared using the two types of batter. (b) Construct a 99% confidence interval for the difference between the average densities for the two mixes. (Round your answers to three decimal places.)