A tire manufacturer tested the braking performance of one of its tire models on a test track. The company tried the tires on 10 different cars, recording the stopping distance for each car on both wet and dry pavement. Results are shown in the table.

a) Write a 95% confidence interval for the mean dry pavement stopping distance. Be sure to check the appropriate assumptions and conditions, and explain what your interval means.
b) Write a 95% confidence interval for the mean increase in stopping distance on wet pavement. Be sure to check the appropriate assumptions and conditions, and explain what your interval means.

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Stopping Distance (ft) Dry Wet Car # Pavement Pavement 1 150 2 147 3136 4 134 5 130 6 134 7 134 8128 9 136 10 158 201 220 192 146 182 173 202 180 192 206