A random sample of 50 records yields a 95% confidence interval of 21.5 to 23.0 years for the mean age at first marriage of women in a certain county. Explain what is wrong with each of the following interpretations of this interval.
a. If random samples of 50 records were repeatedly selected, then 95% of the time the sample mean age at first marriage for women would be between 21.5 and 23.0 years.
b. Ninety-five percent of the ages at first marriage for women in the county are between 21.5 and 23.0 years.
c. We can be 95% confident that x is between 21.5 and 23.0 years.
d. If we repeatedly sampled the entire population, then 95% of the time the population mean would be between 21.5 and 23.5 years.