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September 13th, 2017, 08:06 AM   #1
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Help with interpreting confidence intervals

I need to do a two sample t test and I have shown my working out below:

State: Does taking an elderberry supplement reduce the number of 'cold' days?
Formulate:
We want to compare mean reduction of cold days with elderberry (µ1) vs a placebo (µ2)
We will test the hypotheses:
H0: µ1 = µ2
H1: µ1 ≠ µ2
α = 0.05
Solve:

The samples are random and independent.
From the Normal probability plots, the P-values for both groups are > 0.05. Thus, assume Normality.
We have the requirements for a two-sample t-test.

I used Minitab to obtain the t-test statistic and P-value:
From the Minitab output, the t-test statistic is -2.07 which follows a t distribution with 26 degrees of freedom. The corresponding P-value is 0.049
Decision: Since the P-value = 0.049 < 0.05, Ho is rejected

Conclusion:

At 5% significance level, there is enough evidence to conclude that there is a difference in the mean number of cold days between the two treatment groups.
The result was significant at 5% level.

Interpreting 95% confidence interval:
95% confidence interval (-4.54, -0.01) obtained from Minitab
We are 95% confident that the difference in the population mean number of cold days of elderberry and placebo is between -4.54 and -0.01 days.
Since both confidence limits are negative, the elderberry appears to be effective in reducing the population mean number of cold days.

I'm not sure if my interpretation of the confidence interval was correct. How do i know if the 'negative' confidence limits favours elderberry or the placebo?
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