Consider a scenario where two vaccines have been developed and their effectiveness was tested by comparing the mean outcome for a vaccinated group to the mean for a control (placebo) group. Both of the vaccine studies set the significance (a) level for the test at .05, two-tailed, and both found statistically significant differences (i.e., the p-value was very small and Ho was rejected). The results were as follows: t-statistic Effect size (d) Study Vaccine 1 0.7 4.8

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2. Consider a scenario where two vaccines have been developed and their effectiveness was tested by
comparing the mean outcome for a vaccinated group to the mean for a control (placebo) group. Both of
the vaccine studies set the significance (a) level for the test at .05, two-tailed, and both found statistically
significant differences (i.e., the p-value was very small and Ho was rejected). The results were as follows:
Study
Effect size (d)
t-statistic
Vaccine 1
0.7
4.8
Vaccine 2
0.2
4.8
(a) Based on the above information, can we know whether one study involved a larger sample size
than the other? If so, which one? Explain.
(b) Based on the above information, can we conclude that one vaccine is preferable to (i.e., more
effective than) the other? If so, which one? Explain.
Transcribed Image Text:2. Consider a scenario where two vaccines have been developed and their effectiveness was tested by comparing the mean outcome for a vaccinated group to the mean for a control (placebo) group. Both of the vaccine studies set the significance (a) level for the test at .05, two-tailed, and both found statistically significant differences (i.e., the p-value was very small and Ho was rejected). The results were as follows: Study Effect size (d) t-statistic Vaccine 1 0.7 4.8 Vaccine 2 0.2 4.8 (a) Based on the above information, can we know whether one study involved a larger sample size than the other? If so, which one? Explain. (b) Based on the above information, can we conclude that one vaccine is preferable to (i.e., more effective than) the other? If so, which one? Explain.
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