State null and alternative hypothesis for 2-sample t-test

In summary, a 2-sample t-test is a statistical test used to compare the means of two independent groups. The null hypothesis states that there is no significant difference between the two groups, while the alternative hypothesis states that there is a significant difference. The test is performed by calculating a t-statistic and comparing it to a critical value. The assumptions of normal distribution, equal variances, and independence must be met for the test to be valid.
  • #1
Deathfish
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Homework Statement



A new type of medical tubing is being developed by company ABC. The development engineer would like to test whether the tube has better elongation than the competitor's design.

State the hypotheses that should be tested in this experiment

The Attempt at a Solution



Ho: The new tubing has the same elongation or worse than competitor's design
μ1 ≤ μ2

Ha: The new tubing has better elongation than competitor's design (claim)
μ1 > μ2

i got this wrong, can't figure out why
 
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  • #2
Deathfish said:

Homework Statement



A new type of medical tubing is being developed by company ABC. The development engineer would like to test whether the tube has better elongation than the competitor's design.

State the hypotheses that should be tested in this experiment

The Attempt at a Solution



Ho: The new tubing has the same elongation or worse than competitor's design
μ1 ≤ μ2

Ha: The new tubing has better elongation than competitor's design (claim)
μ1 > μ2

i got this wrong, can't figure out why

Seems OK to me.
 

Related to State null and alternative hypothesis for 2-sample t-test

What is the purpose of a 2-sample t-test?

A 2-sample t-test is a statistical test used to compare the means of two independent groups. It is commonly used to determine if there is a significant difference between the two groups in terms of a continuous variable.

What is a null hypothesis in a 2-sample t-test?

The null hypothesis in a 2-sample t-test states that there is no significant difference between the means of the two groups being compared. In other words, any difference observed between the two groups is due to chance or random variation.

What is an alternative hypothesis in a 2-sample t-test?

The alternative hypothesis in a 2-sample t-test states that there is a significant difference between the means of the two groups being compared. This means that the observed difference between the two groups is not due to chance and is likely a real difference.

How is a 2-sample t-test performed?

To perform a 2-sample t-test, the data from the two groups are compared using a t-statistic, which is calculated by dividing the difference between the two sample means by the standard error of the difference. The resulting t-value is then compared to a critical value from a t-table, and if the t-value is greater than the critical value, the null hypothesis is rejected in favor of the alternative hypothesis.

What are the assumptions of a 2-sample t-test?

There are several assumptions that must be met in order for a 2-sample t-test to be valid. These include: the data in each group are normally distributed, the variances of the two groups are equal, and the two groups are independent of each other. Violating these assumptions can lead to inaccurate results.

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