Answer:
(1.218 ; 1.322)
the confidence interval is appropriate
Step-by-step explanation:
The confidence interval :
Mean ± margin of error
Sample mean = 1.27
Sample standard deviation, s = 0.80
Sample size, n = 914
Since we are using tbe sample standard deviation, we use the T table ;
Margin of Error = Tcritical * s/√n
Tcritical at 95% ; df = 914 - 1 = 913
Tcritical(0.05, 913) = 1.96
Margin of Error = 1.96 * 0.80/√914 = 0.05186
Mean ± margin of error
1.27 ± 0.05186
Lower boundary = 1.27 - 0.05186 = 1.218
Upper boundary = 1.27 + 0.05186 = 1.322
(1.218 ; 1.322)
According to the central limit theorem, sample means will approach a normal distribution as the sample size increases. Hence, the confidence interval is valid, the sample size of 914 gave a critical value at 0.05 which is only marginally different from that will obtained using a normal distribution table. Hence, the confidence interval is appropriate
