Answer: (4.95, 4.99)
Explanation: This question simply wants us to construct a 95% confidence level for the population mean of pressure controller.
n = sample size = 19
x = sample mean = 4.97
s = sample standard deviation = 0.0461
To construct a confidence interval for mean, we need a critical value for a two tailed test, for this question we will make use of a t tail test to get our critical value because sample standard deviation is given and sample size is less than 30 (19).
At 95% confidence interval, it implies that our level of significance (α) is 5%.
The 95% confidence interval for mean is given below as
Upper limit
u = x + tα/2 × (s/√n)
Lower limit
u = x - tα/2 × (s/√n)
The value of tα/2 is gotten using a t test table and from the table , we have tα/2 as 2.10092
By substituting the parameters, we have that
For upper limit
u = 4.97 + 2.10092 × 0.0461/√19
u = 4.97 + (2.10092 ×0.0106)
u = 4.97 + 0.0222
u = 4.99
For lower limit
u = 4.97 - 2.10092 × 0.0461/√19
u = 4.97 - (2.10092 ×0.0106)
u = 4.97 -0.0222
u = 4.95
Confidence interval = (4.95, 4.99)
