Commute times in the U.S. are heavily skewed to the right. We select a random sample of 200 people from the 2000 U.S. Census who reported a non-zero commute time. In this sample the mean commute time is 27.5 minutes with a standard deviation of 18.9 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 = = 27.5
Sample standard deviation = s = 18.9
Sample size = n = 200
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/)
= ( 27.5 - 30 ) / ( 18.9 / 200 )
= -1.871
df = n - 1 = 199
P- Value = 0.0314
The p-value is p = 0.0314 < 0.05, it is concluded that the null hypothesis is rejected.
Commute times in the U.S. are heavily skewed to the right. We select a random sample...
Commute times in the U.S. are heavily skewed to the right. We select a random sample of 200 people from the 2000 U.S. Census who reported a non-zero commute time. In this sample the mean commute time is 27.5 minutes with a standard deviation of 18.9 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...
Commute times in the U.S. are heavily skewed to the right. We select a random sample of 200 people from the 2000 U.S. Census who reported a non-zero commute time. In this sample the mean commute time is 27.5 minutes with a standard deviation of 18.9 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...
Commute times in the U.S. are heavily skewed to the right. We select a random sample of 200 people from the 2000 U.S. Census who reported a non-zero commute time. In this sample the mean commute time is 27.5 minutes with a standard deviation of 18.9 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...
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