Answer:
The confidence interval is
Step-by-step explanation:
From the question we are given a data set
25.5, 26.1, 26.8, 23.2, 24.2, 28.4, 25.0, 27.8, 27.3, and 25.7.
The mean of the this sample data is
where is the sample size with values n = 10
The standard deviation is evaluated as
substituting values
The confidence level is given as 90% hence the level of significance is calculated as
%
Now the critical values of is obtained from the normal distribution table as
The reason we are obtaining the critical values of instead of
is because we are considering two tails of the area under the normal curve
The margin of error is evaluated as
substituting values
The 90%, two sided confidence interval is mathematically evaluated as
Given that the lower and the upper limit is greater than 25 then we can assure the manufactures that the battery life exceeds 25 hours