Question

construct a confidence inteval to estimate the difterence ander. The Winnipeg. of the two cities. whether the true meesonert? interval for he the Winnipes ap and (−50,250). iect H 0​ at the 1% level re 98% con fide to relect H 2 at the 2% level

Answer 1

To construct a confidence interval to estimate the difference between the means of two cities, follow these steps: Determine the confidence level, find the critical value, calculate the margin of error, and then find the confidence interval using the sample mean and margin of error.

Step-by-step explanation:

To construct a confidence interval to estimate the difference between the means of two cities (Winnipeg and another city), we need the sample mean, sample standard deviation, sample size, and confidence level. Using the given information, the confidence interval can be calculated as follows:

1. Given the confidence level is 98% (CL = 0.98), the alpha level is 1 - CL = 0.02.
2. Convert the alpha level to a Z-score by finding the critical value for a two-tailed test. In this case, the critical value is Z = ±2.33.
3. Calculate the margin of error (ME) using the formula: ME = Z * (standard deviation / √n).
4. Substitute the values into the formula to find the confidence interval: CI = (sample mean - ME, sample mean + ME).
5. Based on the given data, the confidence interval for the true mean difference between the cities is (-50,250) ± ME.