Question 967336: 4. The IRS claims that it takes 87 minutes to prepare a tax form. You believe it takes longer than 87 minutes. You ask 19 tax filers and find the following preparation times:
61, 74, 78, 79, 87, 88, 96, 97, 98, 98, 99, 100, 100, 101, 108, 110, 117, 120, 121
Determine if the preparation time is significantly longer than 87 minutes. Use α = .025.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! 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 this calculator, 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.
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