10 ---### Monitoring Bear Population HealthThe health of the bear population in a park is monitored by periodic measurements taken from anesthetized bears. A sample of the weights of these bears is provided below. The task is to find a 95% confidence interval estimate of the mean of the population for all such bear weights.#### Data Table:- 78- 342- 414- 346- 164- 218- 260- 358- 202- 142- 330- 32- 138- 178#### Confidence Interval CalculationThe 95% confidence interval for the mean bear weight is expressed as:\[ A < \mu < B \]Where,- \( A = \_\_\_\_\_\_\_\_ \)- \( B = \_\_\_\_\_\_\_\_ \)In this exercise, you'll calculate the values of \( A \) and \( B \) to understand the range in which the true mean weight of the entire bear population is likely to be found, with 95% confidence.---This format is designed for educational purposes, providing students with an opportunity to engage with statistical concepts and apply them to real-world data.

from the given data table : Sample Size, n = 14 Sample Mean, x̄ = 228.71429 sample standard deviation, s = 115.56578 confidence level,c= 0.95solution : Significance level, α =1- 0.95 = 0.05 Degree of freedom df = n-1 = 13 critical value : critical value at α= 0.05 and df= 13 is tα/2,df= 2.16 .....from student's t distribution table 95% confidence interval = 228.71429 ± 2.16 x 115.56578 / √ 14 = 228.71429 ± 66.714308 (= 228.71429 - 66.714308 , 228.71429 + 66.714308 ) = ( 162.0 , 295.4286 ) A < u <B where A = Lower limit = 162 B = Upper limit = 295.4286