In section 2F, we learned about two-population confidence intervals. However new statistics students usually have a difficult time explaining them and often make incorrect statements about the confidence intervals.

Answer the following questions in your initial post. Then respond to at least two or more of your classmates. Remember to be kind and respectful.

1. How do we know if a population parameter from population 1 is significantly higher, significantly lower, or not significantly different than population 2?

Look at the following two-population confidence interval example calculated from data from a business. The data came from random samples and passed all of the assumptions. Use this printout to answer questions #2-6.

95% confidence level

Population 1: population mean average salary for part-time employees in dollars per hour.

Population 2: population mean average salary for full-time employees in dollars per hour.

Sample Difference: - $2.36 (Sample mean average salary for part-time employees was $2.36 less than for full-time employees.)

Margin of Error: $0.82

Confidence Interval Lower Limit: - $3.18

Confidence Interval Upper Limit: - $1.54

Confidence Interval: ( -$3.18 , -$1.54 )

2.

How did the computer use the sample difference ( - $2.36 ) and the margin of error ( $0.82 ) to calculate the upper and lower limits of the confidence interval?

3.

A statistics student was asked if the population mean average salary for part-time employees was significantly higher, significantly lower or not significantly different than for full time employees. The statistics student said, "I am 95% confident that the population mean average salary for population 1 (part-time employees) is significantly LOWER than the population mean average salary for population 2 (full-time employees). This is absolutely correct! How did the statistics student know this?

4.

A statistics student says that the the population mean average salary for all part-time employees is exactly $2.36 less than the population mean average salary for full-time employees. This is totally wrong. Why do you think statistics students make this mistake?

5.

A statistics student says that the population mean average salary for part-time employees is exactly $1.54 per hour and the population mean average salary for full-time employees is $3.18 per hour. This is totally wrong. Why do you think statistics students make this mistake?

6.

A statistics student was asked much lower could the population mean average salary for all part-time employees be than the population mean average salary for all full-time employees? The statistics student said, "I do not know exactly how much lower since I only have sample data. I can say that I am 95% confident that the population mean average salary for part-time employees at this company is between $1.54 and $3.18 lower than for full-time employees". Explain why this is the correct interpretation of the confidence interval.

Please type explanation