The range for the average age of all site visitors is found to be between 21.15 and 23.55.
<h3>Define the term confidence interval?</h3>
- The likelihood that a quantity will fall between two values near the mean is shown by a confidence interval.
- Confidence intervals quantify how certain or uncertain a sampling technique is.
- They are also utilized in regression analysis and hypothesis testing.
For the given question;
Confidence interval CI = 90% = 0.9
Sample size n = 56 users
Mean (x) = 22.5 years years
Standard deviation (s) = 5 years
Then formula for the CI is given as,
CI = x + z.s/√n
The steps included are-
1. Subtract 1 from sample size to get the degree of freedom df:
df = 56 - 1 = 55
2. To get teh alpha level.
α = (1 - 0.9)/2 = 0.05
3: check df and α in t-distribution to get z score.
z = 2.003
4: To get sample size,
S = s/√n
S = 5/√56
S = 0.66
z x S = 0.66 x 2.033 = 1.35
5: To get the lower range subtract 1.35 from sample mean
22.5 - 1.35 = 21.15
6:n To get the upper range, add t 1.35 from sample mean.
22.5 + 1.35 = 23.55
Thus, the confidence interval is 21.15 and 23.55.
To know more about the confidence interval, here
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