Final answer:
To find the critical value for a chi-square or t-distribution with a 90% confidence level and a sample size of 15, you would refer to the appropriate distribution table using 14 degrees of freedom. However, the notation 'x2r' is atypical, and further clarification may be needed to provide the most accurate assistance.
Step-by-step explanation:
Finding the Critical Value for a Given Confidence Level
To find the critical value x2r corresponding to a sample size of 15 and a confidence level of 90%, you'll need to refer to a chi-square distribution table since the question seems to imply a chi-square distribution (though the term 'x2r' is not standard). Typically, for a chi-square distribution, the degrees of freedom (df) are calculated as the sample size minus 1, which in this case is 15 - 1 = 14. However, since each situation may vary, and because the information may not be complete, it's important to use the correct table for chi-square, t-distribution, or z-distribution based on the context of the question. If the context requires using the chi-square distribution, look for the row corresponding to 14 degrees of freedom and find the value that lines up with the 90% confidence level column.
If, on the other hand, we are dealing with a t-distribution (which might be suggested by the context of critical values and confidence levels), for 14 degrees of freedom and a 90% confidence level, the critical t-value would usually be two-sided and you would refer to a t-table to find the exact value. However, it's worth noting that 'x2r' is not a standard notation for a critical value in statistical testing, so further clarification from the student would improve the accuracy of the help provided.