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Find tα/₂when n = 12 for the 95% confidence interval for the mean.

A) 1.80
B) 2.92
C) 2.20
D) 1.52

1 Answer

6 votes

Final answer:

The t statistic (tα/2) for a 95% confidence interval with a sample size of 12 is approximately 2.20, which matches option C from the provided choices.

Step-by-step explanation:

The student's question refers to finding the t statistic (tα/2) for constructing a 95% confidence interval for the mean when the sample size (n) is 12. Since the sample size is given, the degrees of freedom (df) will be n - 1, which is 11.

For a 95% confidence level and 11 degrees of freedom, we need to find the critical t value that leaves a total area of 5% (or 0.05 in probability terms) in the two tails of the t-distribution.

Consulting a t-distribution table or using statistical software or a calculator with invT functionality, we can determine the t statistic. Typically, for a 95% confidence interval with 11 degrees of freedom, the correct t value will be approximately 2.201.

However, the response options provided are: A) 1.80, B) 2.92, C) 2.20, D) 1.52. Among these, option C) 2.20 is the closest to the correct critical t value.

The 95 percent confidence interval for the mean (μ) is given by:

(x - tλ/2 * s/sqrt(n), x + tλ/2 * s/sqrt(n))

where x is the sample mean, s is the sample standard deviation, n is the sample size, and tλ/2 is the t-value corresponding to the desired confidence level and degrees of freedom.

In this case, n = 12, and the 95% confidence level corresponds to a t-value of approximately 2.18. Therefore, the answer is not provided in the given options.

User Schore
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