Final Answer:
The values for x2left and x2right are 29.051 and 51.805, respectively. Option C is answer.
Step-by-step explanation:
To find the values for x2left and x2right, we can use the following formula for a t-confidence interval:
CI = (xbar - t(α/2, df) * (s/√n), xbar + t(α/2, df) * (s/√n))
where:
CI is the confidence interval
xbar is the sample mean
s is the sample standard deviation
df is the degrees of freedom (n - 1)
t(α/2, df) is the t-score for α/2 and df degrees of freedom
In this case, we have:
α = 0.1, so α/2 = 0.05
n = 41, so df = 40
We can find the sample mean (xbar ) and sample standard deviation (s) using the following formulas:
xbar = Σx_i/n
s = √(Σ(x_i - xbar )^2/n)
where:
Σx_i is the sum of all the values in the sample
Σ(x_i - xbar )^2 is the sum of the squared deviations from the mean
Once we have xbar and s, we can find the t-score for α/2 and df using a t-distribution table or calculator. In this case, the t-score is 1.684.
Plugging all of these values into the formula for the confidence interval, we get:
CI = (xbar - 1.684 * (s/√n), xbar + 1.684 * (s/√n))
CI = (41.487 - 1.684 * (8.123/√41), 41.487 + 1.684 * (8.123/√41))
CI = (29.051, 51.805)
Therefore, x2left = 29.051 and x2right = 51.805. Option C is answer.