Step 1 :We are given that the sample mean (\(\bar{x}\)) is 3.4, the standard deviation (s) is 2.7, and the sample size (n) is 234. The confidence level is 90%, so the Z-score is approximately 1.645.
Step 2 :We can use these values to calculate the margin of error for the confidence interval. The formula for the margin of error is \(Z \frac{s}{\sqrt{n}}\).
Step 3 :Substituting the given values into the formula, we get \(1.645 \frac{2.7}{\sqrt{234}}\).
Step 4 :Calculating the above expression, we get the margin of error to be approximately 0.290.
Step 5 :We can now calculate the confidence interval. The formula for the confidence interval is \(\bar{x} \pm \) margin of error.
Step 6 :Substituting the given values into the formula, we get \(3.4 \pm 0.290\).
Step 7 :Calculating the above expression, we get the confidence interval to be between 3.110 and 3.690.
Step 8 :\(\boxed{\text{Final Answer: With 90% confidence, the population mean number of visits per week is between 3.110 and 3.690 visits.}}\)