Question

In: Statistics and Probability

You randomly select 22 student cars and find they have a mean age of 8 years...

You randomly select 22 student cars and find they have a mean age of 8 years and a standard deviation of 3.4 years. You also randomly select 28 faculty cars and find they have a mean age of 5.3 years and a standard deviation of 3.7 years.

Use a 0.01 significance level to test the claim that student cars are older than faculty cars.

(a) test statistic
(b) the p-value

Solutions

Expert Solution

The Hypothesis:

H0: =

Ha: >

This is a right tailed test

____________________

Since s1/s2 = 3.4/3.7 = 0.91 (it lies between 0.5 and 2) we used the pooled variance.

The degrees of freedom used is n1 + n2 - 2 = 22 + 28 - 2 = 48 (since pooled variance is used)

_________________

The Test Statistic:

__________________

The p Value:    The p value (Right Tail) for t = 2.68 ,df = 48,is; p value = 0.005

_________________

The Decision Rule: If the P value is < , Then Reject H0

The Decision:    Since P value (0.005) is < (0.01), We Reject H0.

The Conclusion: There is sufficient evidence at the 99% significance level to conclude that the students cars are older than faculty cars.


Related Solutions

You randomly select 22 student cars and find they have a mean age of 8 years...
You randomly select 22 student cars and find they have a mean age of 8 years and a standard deviation of 3.4 years. You also randomly select 28 faculty cars and find they have a mean age of 5.3 years and a standard deviation of 3.7 years. Use a 0.01 significance level to test the claim that student cars are older than faculty cars. (a) test statistic (b) the p-value
Randomly selected 22 22 student cars have ages with a mean of 7.2 7.2 years and...
Randomly selected 22 22 student cars have ages with a mean of 7.2 7.2 years and a standard deviation of 3.6 3.6 years, while randomly selected 27 27 faculty cars have ages with a mean of 5.1 5.1 years and a standard deviation of 3.5 3.5 years. 1. Use a 0.01 0.01 significance level to test the claim that student cars are older than faculty cars. (a) The test statistic is (b) The critical value is (c) Is there sufficient...
Randomly selected 23 student cars have ages with a mean of 8 years and a standard...
Randomly selected 23 student cars have ages with a mean of 8 years and a standard deviation of 3.6 years, while randomly selected 27 faculty cars have ages with a mean of 5.8years and a standard deviation of 3.7 years. 1. Use a 0.01significance level to test the claim that student cars are older than faculty cars. (a) The test statistic is (b) The critical value is (c) Is there sufficient evidence to support the claim that student cars are...
Randomly selected 24 student cars have ages with a mean of 8 years and a standard...
Randomly selected 24 student cars have ages with a mean of 8 years and a standard deviation of 3.6 years, while randomly selected 30 faculty cars have ages with a mean of 6 years and a standard deviation of 3.3 ears. 1. Use a 0.01 significance level to test the claim that student cars are older than faculty cars. (a) The test statistic is ___________ (b) The critical value is ___________ (c) Is there sufficient evidence to support the claim...
Randomly selected 8080 student cars have ages with a mean of 88 years and a standard...
Randomly selected 8080 student cars have ages with a mean of 88 years and a standard deviation of 3.6 years, while randomly selected 9595 faculty cars have ages with a mean of 5.4 years and a standard deviation of 3.7 years. 1.    Use a 0.03 significance level to test the claim that student cars are older than faculty cars. The test statistic is   The critical value is   Is there sufficient evidence to support the claim that student cars are older than...
Randomly selected 2929 student cars have ages with a mean of 77 years and a standard...
Randomly selected 2929 student cars have ages with a mean of 77 years and a standard deviation of 3.43.4 years, while randomly selected 1515 faculty cars have ages with a mean of 5.95.9 years and a standard deviation of 3.73.7 years. 1. Use a 0.010.01 significance level to test the claim that student cars are older than faculty cars. (a) The null hypothesis is H0:μs=μfH0:μs=μf. What is the alternate hypothesis? A. HA:μs<μfHA:μs<μf B. HA:μs≠μfHA:μs≠μf C. HA:μs>μfHA:μs>μf (b) The test statistic...
Randomly selected 140 student cars have ages with a mean of 7.5 years and a standard...
Randomly selected 140 student cars have ages with a mean of 7.5 years and a standard deviation of 3.6 years, while randomly selected 75 faculty cars have ages with a mean of 5.4 years and a standard deviation of 3.5 years. 1. Use a 0.03 significance level to test the claim that student cars are older than faculty cars. The test statistic is The critical value is Is there sufficient evidence to support the claim that student cars are older...
A sample of 21 randomly selected student cars have ages with a mean of 7.5 years...
A sample of 21 randomly selected student cars have ages with a mean of 7.5 years and a standard deviation of 3.4 years, while a sample of 32 randomly selected faculty cars have ages with a mean of 5.5 years and a standard deviation of 2.8 years. First, define student cars as Population 1 and faculty cars as Population 2. Thus we have n1=21, n2=32, x¯1=7.5, x¯2=5.5, s1=3.4, s2=2.8, (a) Based on the study data, is there significant evidence that...
Randomly selected 30 student cars have ages with a mean of 7 years and a standard...
Randomly selected 30 student cars have ages with a mean of 7 years and a standard deviation of 3.6 years, while randomly selected 23 faculty cars have ages with a mean of 5.9 years and a standard deviation of 3.5 years. 1. Use a 0.01 significance level to test the claim that student cars are older than faculty cars. (a) The test statistic is (b) The critical value is (c) Is there sufficient evidence to support the claim that student...
A sample of 30 randomly selected student cars have ages with a mean of 7.3 years...
A sample of 30 randomly selected student cars have ages with a mean of 7.3 years and a standard deviation of 3.6 years, while a sample of 19 randomly selected faculty cars have ages with a mean of 5 years and a standard deviation of 3.7 years. 1. Use a 0.01 significance level to test the claim that student cars are older than faculty cars. (a) The test statistic is ??? (b) The critical value is ??? (c) Is there...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT