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A researcher reports a 95% CI 2.30, 2.50. If the null hypothesis were that the mean in the populaiton equals 2.00, then what would the decision have been for a significance test at a .05 level of significance?

a. Retain the null because 2.00 is not contained in the confidence interval.

b. Reject the null because 2.00 is not contained in the confidence interval.

c. Retain the null because 2.00 is contained in the confidence interval.

d. Reject the null because 2.00 is contained in the confidence interval.

Answer :

Final answer:

Based on the provided 95% confidence interval (2.30, 2.50),

(b) the null hypothesis that the population mean equals 2.00 would be rejected, as it falls outside of this interval.

Explanation:

In hypothesis testing,

if a value (in this case, 2.00) is outside of the 95% confidence interval (2.30, 2.50),

we reject the null hypothesis.

This is because the confidence interval contains the range of values we would expect the population mean to lie within, given our sample data.

Since 2.00 is beneath our lower limit of 2.30, it falls outside of this interval.

Therefore, the decision in this case would have been to reject the null hypothesis.

Thus, the correct option is (b) Reject the null because 2.00 is not contained in the confidence interval.

Learn more about Hypothesis Testing here:

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