Commute times in the U.S. are heavily skewed to the right. We select a random sample of 220 people from the 2000 U.S. Census who reported a non-zero commute time.
In this sample the mean commute time is 28.3 minutes with a standard deviation of 19.2 minutes. Can we conclude from this data that the mean commute time in the U.S. is less than half an hour? Conduct a hypothesis test at the 5% level of significance.
What is the p-value for this hypothesis test?
Your answer should be rounded to 4 decimal places.
Solution :
Given that,
Population mean = = 30
Sample mean = = 28.3
Sample standard deviation = s = 19.2
Sample size = n = 220
Level of significance = = 0.05
This is a left (One) tailed test,
The null and alternative hypothesis is,
Ho: 30
Ha: 30
The test statistics,
t = ( - )/ (s/)
= ( 28.8 - 30 ) / ( 19.2 / 220 )
= -1.313
df = n - 1 = 219
P- Value = 0.0952
The p-value is p = 0.0952 > 0.05, it is concluded that the null hypothesis is fail to rejected.
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