The average cost per night of a hotel room in New York City is $272 (SmartMoney, March 2009). Assume this estimate is based on a sample of 45 hotels and that the sample standard deviation is $65.

Anyway, http://davidmlane.com/hyperstat/z_table.html

To calculate the average cost per night of a hotel room in New York City, we need to find the mean or average.

Step 1: Write down the given values.
Sample size (n) = 45
Sample mean (x̄) = $272
Sample standard deviation (σ) = $65

Step 2: Use the formula to calculate the standard error (SE).
The formula for standard error is: SE = σ / √n

SE = 65 / √45 ≈ 9.67

Step 3: Calculate the margin of error (MoE).
The margin of error is typically represented by 2 multiplied by the standard error. So, MoE = 2 * SE

MoE ≈ 2 * 9.67 ≈ 19.34

Step 4: Calculate the confidence interval (CI).
When estimating a population parameter, it is common to calculate a confidence interval. A commonly used confidence level is 95%.

To calculate the confidence interval, we subtract and add the margin of error to the sample mean.

Lower bound = sample mean - MoE
Lower bound = 272 - 19.34 ≈ 252.66

Upper bound = sample mean + MoE
Upper bound = 272 + 19.34 ≈ 291.34

So, the 95% confidence interval for the average cost per night of a hotel room in New York City is approximately $252.66 to $291.34.