Arandom sample of 100 records yields a 95% confidence interval for the mean age at first marriage of women in a certain country of 20.5 to 24.0 years. Explain what is wrong with each of the following interpretations of this interval.

(a) If random samples of 100 records were repeatedly selected, then 95% of the time the sample mean age at first marriage for women would be between 20.5 and 24.0 years.

(b) Ninety-five percent of the ages at first marriage for women in the county are between 20.5 and 24.0 years.

(c) We can be 95% confident that ¯y is between 20.5 and 24.0 years.

(d) If we repeatedly sampled the entire population, then 95% of the time the population mean would be between 20.5 and 24.0 years.