Answer:
We are 90% confident that the true mean lies between 8..6563 and 9.9437
Step-by-step explanation:
The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. Confidence is another word for probability.
mean (x) = 9.3
standard deviation (s) = 2
sample size (n) = 28
<u>T- Distribution:</u>
degree of freedom = n - 1 = 28 - 1 = 27
90% Confidence Interval ==> α = 0.1
critical value, t = 1.703 ( t-table)
standard error, SE = s/√n = 2 /√28 = 0.3780
margin of error, E = t × SE= 1.703 × 0.3780 = 0.6437
Confidence Interval: x ± E = 9.3 ± 0.6437
lower limit: x - E = 9.3 - 0.6437 = 8.6563
upper limit: x + E = 9.3 + 0.6437 = 9.9437
Confidence Interval: 8.6563 < µ < 9.9437
<u>Z - Distribution:</u>
Formula: Confidence Interval = x ± z (s/√n)
Sample Mean = s/√n = 2/√28 = 2/5.29 = 0.3781
z = 1.645 (from z - table)
From formula, z (s/√n): 0.3781 x 1.645 = 0.620 (rounded)
x ± 0.62
lower limit: x - 0.62 = 9.3 - 0.62 = 8.68
upper limit: x + 0.62 = 9.3 + 0.62 = 9.92
Confidence Interval: 8.68 < µ < 9.92
Learn more about Confidence Intervals here: brainly.com/question/2141785
