RINTER VERSION BACK Football Air Pressune During the National Football League\'s
ID: 3340511 • Letter: R
Question
RINTER VERSION BACK Football Air Pressune During the National Football League's 2014 AFC championship game, officials measured the air pressure on 11 of the game foothballs 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. Assurhing this is a represeritative sample of all footballs used by the Patriots in the 2014 season, perform the appropriate test to determine f 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 p2 - 41-2 p p1 p2 12.5 Select a Print VS 0Explanation / Answer
Solution:-
a) State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: > 12.5
Alternative hypothesis: < 12.5
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a one-sample t-test.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
b)
SE = s / sqrt(n)
S.E = 0.1206
DF = n - 1 = 11 - 1
D.F = 11
t = (x - ) / SE
t = 11.61
where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.
The observed sample mean produced a t statistic test statistic of 11.61.
Thus the P-value in this analysis is less than 0.00001
Interpret results. Since the P-value (almost 0) is less than the significance level (0.01), we have to reject the null hypothesis.
c)
Reject H0.
Yes we have significance evidence that the air pressure is lower than 2.5 psi.
d) Yes.
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