Next, set-up a claim using a comparison of the two means or proportions. Decide if they are significantly different using your descriptive statistics, then align your claim appropriately.
If you find that the two group's means or proportions are significantly different, make a claim that one mean/proportion is higher/lower than the other as the alternative hypothesis. Then conduct the test and select a level of significance to reject the null hypothesis and--in your conclusion--provide the sample as evidence to support the claim.
If you find that the two group's means or proportions are relatively similar, make a claim that there is no significant difference between them. Then select a level of significance to fail to reject the null hypothesis and--in your conclusion--state that the sample does not provide sufficient evidence to reject the claim.
To complete this task, you may need to change previous steps like the scope or findings to make sure the message stays consistent throughout.
Full Answer Section
Formulating the Claim
Based on the descriptive statistics, we can make an initial observation about whether the two groups appear to be different. This observation will guide the claim.
Possible scenarios:
- Means appear significantly different:
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- Claim: The mean of group A is different from the mean of group B.
- Null hypothesis (H0): There is no difference between the means of group A and group B.
- Alternative hypothesis (Ha): The mean of group A is different from the mean of group B.
- Test: Two-sample t-test (assuming equal variances) or independent t-test (assuming unequal variances).
- Proportions appear significantly different:
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- Claim: The proportion of group A is different from the proportion of group B.
- Null hypothesis (H0): There is no difference between the proportions of group A and group B.
- Alternative hypothesis (Ha): The proportion of group A is different from the proportion of group B.
- Test: Two-sample z-test for proportions.
- Means or proportions appear similar:
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- Claim: There is no significant difference between the means (or proportions) of group A and group B.
- Null hypothesis (H0): There is no difference between the means (or proportions) of group A and group B.
- Alternative hypothesis (Ha): The mean (or proportion) of group A is different from the mean (or proportion) of group B.
- Test: Same as above, but the goal is to fail to reject the null hypothesis.
Selecting a Significance Level
The significance level (alpha) determines the probability of rejecting the null hypothesis when it is actually true. Common choices are 0.05 (5%) and 0.01 (1%). A lower alpha level reduces the chance of a Type I error (rejecting a true null hypothesis) but increases the chance of a Type II error (failing to reject a false null hypothesis).
Conducting the Test and Drawing Conclusions
Using statistical software, perform the chosen hypothesis test. Compare the calculated p-value to the significance level.
- If p-value <= alpha: Reject the null hypothesis and conclude that there is a significant difference between the groups.
- If p-value > alpha: Fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a difference between the groups.
Example
Conclusion:
- "Based on the sample data and a significance level of 0.05, we reject the null hypothesis and conclude that there is a significant difference in mean salaries between the two groups, with Group A earning significantly more than Group B."
Or,
- "Based on the sample data and a significance level of 0.05, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a significant difference in the proportion of college graduates between the two groups."