A sports writer wants to see if a football filled with helium travels farther, on average, than a football filled with air. 15 footballs were filled with helium to the recommend pressure and 11 footballs were filled with air to the recommended pressure. The mean yardage for the helium filled footballs was 232 yards with a standard deviation of 2 yards. The mean yardage for the air filled footballs was 261 yards with a standard deviation of 4 yards. Assume the populations are normal with equal variances. Required:
a. Construct a 80% confidence interval for the mean difference in in yardage for the two types of footballs Lower bound
b. What can you conclude about the sports writer's idea that helimum footballs travel farther, on average?