Final answer:
The critical value for constructing a 90% confidence interval with 4 degrees of freedom is approximately 2.132. This value should be used along with the sample mean and standard deviation to calculate the confidence interval for the mean noise level at airports based on the given data.
Step-by-step explanation:
The student's question is about constructing a 90% confidence interval for the mean noise level at airports based on a given set of decibel measurements. To find the critical value for constructing the confidence interval, we need to refer to the t-distribution table, as the population standard deviation is unknown and the sample size is small.
Given that we are constructing a 90% confidence interval and our sample size is 5, we have 4 degrees of freedom (n-1). For a two-tailed test at the 90% confidence level, the critical t-value with 4 degrees of freedom is approximately 2.132, according to the t-distribution table. This is the critical value that should be used in constructing the confidence interval.
To construct the confidence interval, we will need to calculate the sample mean and sample standard deviation using the given data points (117, 118, 140, 116, 119). The formula for the confidence interval is: mean ± (critical value) * (standard deviation / √n), where √n is the square root of the sample size.