A finger-tapping experiment was conducted by a doctoral neuropsychology student. The purpose of this experiment was to determine bilateral nervous system integrity, which provides data about the neuromuscular system and motor control. The experiment requires the subjects to place the palm of the hand on a table and then to tap the index finger on the surface of the table. Ten subjects who had suffered a mild concussion were given a finger tapping test using the right index finger and then the left index finger. The total number of taps in 30 seconds by each subject are listed in the following table. All subject in the data set are right-handed. Assume that the population of paired differences is approximately normally distributed.

a. Make a 95% confidence interval for the mean of the population of paired differences, where a paired difference is equal to the number of taps for the right index finger minus the number of taps for the left index finger.
b. Using a 5% significance level, can you conclude that the average number of taps is different for the right and left index fingers?

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Subject 8 9 3 4 5 6 10 Right 125 131 127 138 95 91 105 137 129 112 138 94 107 130 128 Left 97 85 114 135 85 3.