Dalton Castene is a public school teacher in Burlington. After a conversation with a colleague in Sudbury, Dalton realizes that his salary is much lower than his colleague's, even though they have similar backgrounds and work experiences. Dalton theorizes that the population mean annual salary for a public school teacher in Burlington is less than the population mean annual salary for a public school teacher in Sudbury. He conducts research on the inquiry and assumes that the population standard deviation is$2,409

for Burlington and$3,192

for Sudbury. Dalton randomly selects the salaries of public school teachers in Burlington and in Sudbury. The results of Dalton's findings are shown in the table below. Explain whether a hypothesis test for the difference between two means of independent samples is appropriate, and if so, find the null and alternative hypotheses, where

1

is the population mean annual salary for a public school teacher in Burlington and

2

is the population mean annual salary for a public school teacher in Sudbury.

BurlingtonSudburyx

x1=$54,906

n1=26

x2=$56,561

n2=22

Select the correct answer below:

Although the population standard deviations are known and the sample sizes are sufficiently large, the samples are not randomly selected and are not independent of each other.

Although the samples are randomly selected, independent, and sufficiently large, the population standard deviation is not known for both districts.

Although the population standard deviations are known and the samples are randomly selected and independent, the sample sizes are not sufficiently large.

All of the conditions to conduct the hypothesis test have been met. The null and alternative hypotheses are

{H0:12=0

Ha:120

.

All of the conditions to conduct the hypothesis test are met. The null and alternative hypotheses are

{H0:12=0

Ha:12>0

.

All of the conditions to conduct the hypothesis test are met. The null and alternative hypotheses are

{H0:12=0

Ha:12<0

.