Question 967336
Given:
mu = 87 (based on the null hypothesis below)
n = 19
alpha = 0.025


Use a calculator to compute the following:
sample mean: xbar = 96.421
sample standard deviation: s = 15.848

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Hypothesis:
H0: mu = 87
H1: mu > 87


Test Statistic:

t = (xbar - mu)/(s/sqrt(n))
t = (96.421 - 87)/(15.848/sqrt(19))
t = 2.591


Now use a calculator to compute the area under the curve to the right of t = 2.591


According to <a href="http://stattrek.com/online-calculator/t-distribution.aspx">this calculator</a>, we find that P(T < 2.591) = 0.9908 (note: degrees of freedom = n-1 = 19-1 = 18)


So this means


P(T > 2.591) = 1 - P(T < 2.591)
P(T > 2.591) = 1 - 0.9908
P(T > 2.591) = 0.0092


This is the p-value.


p-value = 0.0092


Since the p-value (0.0092) is smaller than the value of alpha (0.025), this means we reject the null hypothesis H0.


So we must conclude that the alternative hypothesis H1: mu > 87 is true.


Therefore, we conclude that the average times takes significantly longer than 87 minutes.