The 90% confidence interval for the true mean is (22.79, 24.11).
How to solve
To establish the 90% confidence interval for the true mean spending at the bookstore:
Calculate the standard error: This measures the probable deviation of the sample mean from the actual mean. For this scenario, the standard error, indicating this variance, is about 0.36.
Determine the z-scores: These scores signify how many standard deviations a point differs from the mean. To encompass 90% of the data, z-scores approximately at -1.645 and 1.645 are used.
Compute the confidence interval: By employing these z-scores and the standard error, the margin of error is found.
we have:
The Lower Bound = 23.45 - (-1.645) * 0.36 ≈ 22.79
The Upper Bound = 23.45 + (1.645) * 0.36 ≈ 24.11
Therefore, the 90% confidence interval for the true mean is (22.79, 24.11).