During the national football league’s 2014 afc championship game, officials measured the air pressure on 11 of the game footballs being used by the new england patriots. they found that the balls had an average air pressure of 11.1 psi, with a standard deviation of 0.40 psi.

assuming this is a representative sample of all footballs used by the patriots in the 2014 season, perform the appropriate test to determine if the average air pressure in footballs used by the patriots was significantly less than the allowable limit of 12.5 psi. there is no extreme skewness or outliers in the data, so it is appropriate to use the t-distribution.
(a) clearly state the null and alternative hypotheses.
(b) give the test statistic and p-value and state the conclusion of the test.
2)use a t-distribution to find a confidence interval for the difference in means μ1-μ2 using the relevant sample results from paired data. assume the results come from random samples from populations that are approximately normally distributed, and that differences are computed using d=x1-x2.a 95% confidence interval for μ1-μ2 using the paired difference sample results x¯d=2.9, sd=2.3, nd=30.give the best estimate for μ1-μ2, the margin of error, and the confidence interval. enter the exact answer for the best estimate, and round your answers for the margin of error and the confidence interval to two decimal places.