Question

A sample of salary offers (in thousands of dollars) given to management majors is: 48, 51, 46, 52, 47, 48, 47, 50, 51, and 59. Using this data to obtain a 95% confidence interval resulted in an interval from 47.19 to 52.61. True or False: 95% of all confidence intervals constructed similarly to this one with a sample size of 10 will contain the mean of the population.

Answer 1

True, 95% of all confidence intervals constructed similarly to this one with a sample size of 10 will contain the mean of the population.

Step-by-step explanation:

The statement is True. A 95% confidence interval means that if we were to construct 100 confidence intervals using the same method and sample size, we would expect 95 of them to contain the true population mean. In this case, the 95% confidence interval obtained from the sample of salary offers is (47.19, 52.61), and we can be 95% confident that the true population mean salary lies within this interval.

Answer 2

True.

95% of all confidence intervals constructed similarly to this one with a sample size of 10 will contain the mean of the population.

Step-by-step explanation:

True.

The confidence level represents the proportion of possible confidence intervals that contain the true mean. In this case, 95% of all confidence intervals of sample size n=10 constructed similarly to this one will contain the population mean.