The Tribune claims that the time of travel from downtown to the University via the bus has an average of µ = 27 minutes. A student who normally takes this bus believes that µ is greater than 27 minutes. A sample of six ride times taken to test the hypothesis of interest gave a mean of 27.5 minutes and standard deviation of 2.43 minutes. The value of the test statistic for testing this hypothesis is
- 0.532
0.460
0.504
-0.460
-0.504
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Which of the following conditions doesn't need to be met before you can use a two-sample procedure?
The responses in each group are independent of each other.
Each group is considered to be a sample from a distinct population.
The same variable is measured in both samples.
The goal is to compare the means of the two groups.
Data in two samples are matched together in pairs that are compared.
Well, using a two-sample procedure is like the circus performing with two different acts at the same time. It's quite a balancing act! Now, to answer your question, the condition that doesn't need to be met before using a two-sample procedure is: "Data in two samples are matched together in pairs that are compared." Matching pairs would be more like a dating game show, not a statistical analysis. So, let's cross that one off the list!
The condition that doesn't need to be met before you can use a two-sample procedure is:
Data in two samples are matched together in pairs that are compared.
The value of the test statistic for testing the hypothesis about the average travel time is not directly provided in the question. However, we can calculate it using the given information.
To test if the mean travel time is greater than 27 minutes, we can use a one-sample t-test. The formula for the t-statistic is:
t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))
Plugging in the values from the question:
Sample mean: 27.5 minutes
Hypothesized mean: 27 minutes
Sample standard deviation: 2.43 minutes
Sample size: 6
t = (27.5 - 27) / (2.43 / sqrt(6))
t = 0.5 / (2.43 / sqrt(6))
t = 0.5 / 0.993
t ≈ 0.504
Therefore, the value of the test statistic for testing this hypothesis is approximately 0.504.
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Now, regarding your second question about the conditions for a two-sample procedure:
To use a two-sample procedure, the following conditions should be met:
1. The responses in each group are independent of each other: This condition ensures that the observations in one group do not influence the observations in the other group.
2. Each group is considered to be a sample from a distinct population: The two groups being compared should be distinct populations and not subsets of the same population.
3. The same variable is measured in both samples: The measure being compared should be the same in both groups, such as comparing the mean height of males and females.
4. The goal is to compare the means of the two groups: The purpose of the analysis should be to compare the means of two groups, typically through a hypothesis test or confidence interval estimation.
5. Data in two samples are matched together in pairs that are compared: This condition specifically applies to paired or matched-pair samples, where the data in one sample is matched with the data in the other sample based on certain characteristics, and the differences between the pairs are analyzed.
From the given options, the condition that doesn't need to be met before using a two-sample procedure is: "Data in two samples are matched together in pairs that are compared." This condition is specifically applicable to paired or matched-pair samples but not necessary for all two-sample procedures.
.504010235141
To find the test statistic:
(x - mean)/(sd/√n)
With your data:
(27.5 - 27)/(2.43/√6) = ?
I'll let you finish the calculation.