Final answer:
To conduct a hypothesis test for the average salary of California registered nurses, we can use a t-test since the sample size is small (n=41) and the population standard deviation is unknown. The four possibilities for the hypotheses are: equal, not equal, less than, and greater than. Depending on the alternative hypothesis, a two-tailed test, left-tailed test, or right-tailed test will be used.
Step-by-step explanation:
To conduct a hypothesis test for the average salary of California registered nurses, we can use a t-test since the sample size is small (n=41) and the population standard deviation is unknown.
a. To test if the average salary is equal to $69,110, we use a two-tailed test. The null hypothesis (H0) is that the mean salary of California nurses is $69,110, while the alternative hypothesis (Ha) is that the mean salary is not equal to $69,110.
b. To test if the average salary is different from $69,110, we also use a two-tailed test. The null hypothesis (H0) is that the mean salary is $69,110, while the alternative hypothesis (Ha) is that the mean salary is not equal to $69,110.
c. To test if the average salary is less than $69,110, we use a left-tailed test. The null hypothesis (H0) is that the mean salary is $69,110, while the alternative hypothesis (Ha) is that the mean salary is less than $69,110.
d. To test if the average salary is greater than $69,110, we use a right-tailed test. The null hypothesis (H0) is that the mean salary is $69,110, while the alternative hypothesis (Ha) is that the mean salary is greater than $69,110.