Determining Critical Value for 90% Confidence Interval

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Look at the t tables for n-2 degrees of freedom at the 10% level. Here, we look for a two tailed test with 5-2 = 3 degrees of freedom. This is 2.353.

To determine the critical value necessary to determine a confidence interval for a 90% level of confidence, we need to use the t-distribution table or a statistical software.

In this case, since the sample size is not provided, we will assume that the sample size is small (less than 30) and the population standard deviation is unknown. This implies that we need to use the t-distribution.

The critical value corresponds to the t-score at the tails of the distribution. For a 90% confidence level, we want to find the critical value that leaves 5% in each tail (since the remaining 90% is in the middle).

To find the critical value, we need to determine the degrees of freedom. For small sample sizes, the degrees of freedom are calculated as (n - 1), where n is the sample size.

In this case, we have five data points: (-2, 0), (-1, 0), (0, 1), (1, 1), and (2, 3). Since we have five data points, the sample size (n) is 5. Therefore, the degrees of freedom would be (5 - 1) = 4.

Now, referring to the t-distribution table or using a statistical software, we look up the critical value for a 90% confidence level with 4 degrees of freedom.

Consulting the t-distribution table, we find that the closest value to a 90% confidence level with 4 degrees of freedom is approximately 2.132. Therefore, the correct answer is D. 2.132.

It's important to note that the exact critical value may vary depending on the specific t-distribution table or statistical software used, but the value closest to 2.132 should be the correct answer among the options provided.