Question

The following experiment was run to determine whether or not different flavors of ice cream melt at different speeds. Two flavors (A and B) of ice cream were stored in the same freezer in similar-sized containers. For each observation, one teaspoonful of ice cream was taken from the freezer, transferred to a plate, and the melting time at room temperature was observed to the nearest second. Nine observations were taken on each flavor. These are shown in the following table. Flavor (time in seconds) Pair of data | A | B | Difference 1 | 1009 | 820 | 189 2 | 987 | 970 | 17 3 | 955 | 980 | -25 4 | 1074 | 872 | 202 5 | 994 | 975 | 19 6 | 1040 | 1061 | -21 7 | 1037 | 963 | 74 8 | 999 | 857 | 142 9 | 1013 | 1006 | 7 Number of data | 9 | 9 | 9 Mean | 1012 | 944.9 | 67.1 Standard Deviation | 34.7 | 78.2 | 89.0 (1) Does the data suggest that those two flavors of ice cream melt at different speeds? List your hypothesis and use the two sample t-test (or two population t-test) at significance level 0.01 to test your hypothesis. (2) For the same hypothesis (test whether or not the data suggests that the two flavors of ice cream melt at different speeds), use the paired t-test at significance level 0.01 to test your hypothesis. (3) Based on your paired t-test results, what is the confidence interval for the mean difference between those two flavors of ice cream melt at different speeds?

          The following experiment was run to determine whether or not different flavors of ice cream melt at different speeds. Two flavors (A and B) of ice cream were stored in the same freezer in similar-sized containers. For each observation, one teaspoonful of ice cream was taken from the freezer, transferred to a plate, and the melting time at room temperature was observed to the nearest second. Nine observations were taken on each flavor. These are shown in the following table.

Flavor (time in seconds)
Pair of data | A | B | Difference
1 | 1009 | 820 | 189
2 | 987 | 970 | 17
3 | 955 | 980 | -25
4 | 1074 | 872 | 202
5 | 994 | 975 | 19
6 | 1040 | 1061 | -21
7 | 1037 | 963 | 74
8 | 999 | 857 | 142
9 | 1013 | 1006 | 7
Number of data | 9 | 9 | 9
Mean | 1012 | 944.9 | 67.1
Standard Deviation | 34.7 | 78.2 | 89.0

(1) Does the data suggest that those two flavors of ice cream melt at different speeds? List your hypothesis and use the two sample t-test (or two population t-test) at significance level 0.01 to test your hypothesis.
(2) For the same hypothesis (test whether or not the data suggests that the two flavors of ice cream melt at different speeds), use the paired t-test at significance level 0.01 to test your hypothesis.
(3) Based on your paired t-test results, what is the confidence interval for the mean difference between those two flavors of ice cream melt at different speeds?

The following experiment was run to determine whether or not different flavors of ice cream melt at different speeds. Two flavors (A and B) of ice cream were stored in the same freezer in similar-sized containers. For each observation, one teaspoonful of ice cream was taken from the freezer, transferred to a plate, and the melting time at room temperature was observed to the nearest second. Nine observations were taken on each flavor. These are shown in the following table.

Flavor (time in seconds)
Pair of data | A | B | Difference
1 | 1009 | 820 | 189
2 | 987 | 970 | 17
3 | 955 | 980 | -25
4 | 1074 | 872 | 202
5 | 994 | 975 | 19
6 | 1040 | 1061 | -21
7 | 1037 | 963 | 74
8 | 999 | 857 | 142
9 | 1013 | 1006 | 7
Number of data | 9 | 9 | 9
Mean | 1012 | 944.9 | 67.1
Standard Deviation | 34.7 | 78.2 | 89.0

(1) Does the data suggest that those two flavors of ice cream melt at different speeds? List your hypothesis and use the two sample t-test (or two population t-test) at significance level 0.01 to test your hypothesis.
(2) For the same hypothesis (test whether or not the data suggests that the two flavors of ice cream melt at different speeds), use the paired t-test at significance level 0.01 to test your hypothesis.
(3) Based on your paired t-test results, what is the confidence interval for the mean difference between those two flavors of ice cream melt at different speeds?

Added by Mitchell J.

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