Final answer:
The 90% confidence interval for the mean repair cost requires finding the critical value using a t-distribution with 17 - 1 = 16 degrees of freedom. A t-score of approximately 1.746 is found for a 90% confidence level.
Step-by-step explanation:
To find the 90% confidence interval for the mean repair cost for the TVs, we first need to find the critical value. This involves using the t-distribution since the population standard deviation is unknown and the sample size is relatively small. We need a t-score that corresponds to a 90% confidence level for a two-tailed test with degrees of freedom (df) equal to the sample size minus one (n - 1).
To find the critical t-value, we use degrees of freedom df = 17 - 1 = 16 and look up the critical t-value for a 90% confidence interval in a t-distribution table or use a statistical software. However, if we assume that the population is approximately normal and the sample size is moderate (as in this case with 17 samples), the t-distribution becomes similar to the normal distribution, therefore sometimes a z-score can be used as an approximation. Nevertheless, it is advisable to use a t-score for more accuracy.
If rounding to three decimal places, the t-score for df = 16 at 90% confidence is approximately 1.746 (using a t-distribution table or software).