Confidence Intervals & Hypothesis Testing (2 of 5)

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Ten subjects were tested in the auditory condition and their scores were: 275, 320, 278, 360, 430, 520, 464, 311, 529, and 326.

The 95% confidence interval on the difference between means is:
9 ≤ μvisual - μauditory ≤ 196.
Therefore only values in the interval between 9 and 196 are retained as plausible values for the difference between population means. Since zero, the value specified by the null hypothesis, is not in the interval, the null hypothesis of no difference between auditory and visual presentation can be rejected at the 0.05 level. The probability value for this example is 0.034. Any time the parameter specified by a null hypothesis is not contained in the 95% confidence interval estimating that parameter, the null hypothesis can be rejected at the 0.05 level or less. Similarly, if the 99% interval does not contain the parameter then the null hypothesis can be rejected at the 0.01 level. The null hypothesis is not rejected if the parameter value specified by the null hypothesis is in the interval since the null hypothesis would still be plausible.
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