Testing for Difference in Means with Independent Samples

In summary, the question is whether there is evidence that the difference between the two independent random samples, with 15 and 16 points respectively, is greater than 10. The solution involves using a t-score with 29 degrees of freedom and a 0.01 level of significance. The critical t-score at 0.01 for 29 degrees of freedom is 2.462. To test whether μ2 - μ1 > 10, one can either find the t-score and see how many standard deviations it takes to get 10, or use the t-score to find the critical value and compare it to μ2 - μ1.
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Homework Statement



Independent random samples selected. One has 15 points, one has 16.

It asks "is there evidence μ2 - μ1 > 10? Test at 0.01 level of significance.

2. The attempt at a solution

There are 29 degrees of freedom. The t-score at 0.01 for 29 is 2.462.

I just don't get how I test whether

Homework Statement



Independent random samples selected. One has 15 points, one has 16.

It asks "is there evidence μ2 - μ1 > 10? Test at 0.01 level of significance.

2. The attempt at a solution

There are 29 degrees of freedom. The t-score at 0.01 for 29 is 2.462.

I just don't get how I test whether μ2 - μ1 > 10?

1) Do I just find the t-score, find μ2 - μ1, and see how many standard deviations it takes to get 10, and i.e. if it takes over 3, say very little probablity etc?
 
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  • #2
2) Or do I use the t-score to find the critical value and compare that to μ2 - μ1?Thanks in advance!
 

Related to Testing for Difference in Means with Independent Samples

1. What is the purpose of statistics?

The purpose of statistics is to analyze and interpret data in order to make informed decisions. It allows us to understand and describe a population or sample, identify patterns and trends, and make predictions based on data.

2. What are the different types of data used in statistics?

The two main types of data used in statistics are qualitative data and quantitative data. Qualitative data is descriptive in nature and can be categorized into groups, while quantitative data is numerical and can be measured and analyzed using mathematical methods.

3. How do you determine the central tendency of a data set?

The central tendency of a data set can be determined by calculating the mean, median, or mode. The mean is the average of all the values in the data set, the median is the middle value when the data is arranged in ascending or descending order, and the mode is the most frequently occurring value in the data set.

4. What is the difference between correlation and causation?

Correlation refers to a relationship between two variables where a change in one variable is associated with a change in the other variable. Causation, on the other hand, implies that one variable directly causes a change in the other variable. Correlation does not necessarily imply causation as there could be other factors at play.

5. How do you determine the sample size for a statistical study?

The sample size for a statistical study depends on several factors, such as the desired level of confidence, margin of error, and variability in the data. Generally, a larger sample size will provide more accurate results, but it also requires more time and resources. Sampling techniques and statistical formulas can be used to determine an appropriate sample size for a study.

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