Comparing Weight Gain in Rats: An Analysis of Diets A & B

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A study comparing weight gain in male rats on two different diets, A and B, found that diet A resulted in a significantly higher mean weight gain (99.5 grams) compared to diet B (78.7 grams). An F-test was conducted to compare the sample standard deviations, with the null hypothesis stating that the variances are equal; the calculated F-value was less than the critical value, suggesting the variances can be considered equal. A t-test was then performed to compare the means, confirming that the difference is statistically significant, and a 95% confidence interval was deemed appropriate for interpretation. The discussion also highlighted the importance of determining sample size and the potential use of a paired t-test if raw data were available. Overall, the analysis supports the conclusion that diet A is more effective for weight gain in rats than diet B.
  • #31
I like Serena said:
Yes...

So the interval would be close to zero in the plus and minus direction, something like
(-3, 3)

Like that yeah?
 
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  • #32
Yes! :smile:

So how can you see from your interval whether it is significant or not?
 
  • #33
Because my interval has both boundaries greater than zero, we're 95% certain the difference is between these boundaries, so that means we're 95% certain the difference is greater than zero. This is significant and forces us to reject the null hypothesis?
 
  • #34
Yep! :smile:

When you use a CI in a test to compare the means of two samples, the criterion is whether the CI contains zero.
 
  • #35
Ah I see! :smile:

So it would be better to do a confidence interval instead of a t-test?
 
  • #36
Ah, now we're getting into the murky stuff that is open questions and discussions.

Let me counter that by asking: what are the pro's and con's of a CI versus a t-test?
What's the difference anyhow between a t-test and this confidence interval?

And I'll ask one more question: can you do a 1-sided test with a confidence interval?
 
  • #37
With a CI, we know that if the interval doesn't contain zero the means can't be the same. With a t-test we're relying on probabilities and approximations.

I would sat yes, because if you test Ha: u1>u2, and find a CI for u1-u2, and if this doesn't contain zero we're 95% certain Ha is true
 
  • #38
Maybe_Memorie said:
With a CI, we know that if the interval doesn't contain zero the means can't be the same. With a t-test we're relying on probabilities and approximations.

Wow! Stop!
A CI does not give certainty!
Basically the CI is a t-test. It's just represented differently.
But the ultimate result (rejection or not) is the same.

Maybe_Memorie said:
I would sat yes, because if you test Ha: u1>u2, and find a CI for u1-u2, and if this doesn't contain zero we're 95% certain Ha is true

Hmm, suppose the CI is (-6, -1).
That does not contain 0.
Does that mean Ha is probably true?
 

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