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Registered nurses earned an average annual salary of $69,110. For that same year, a survey was conducted of 41 California registered nurses to determine if the annual salary is higher than $69,110 for California nurses. The sample average was $71,121 with a sample standard deviation of $7,489. Conduct a hypothesis test.

a. Conduct a hypothesis test to determine if the average salary of California registered nurses is equal to $69,110.

b. Conduct a hypothesis test to determine if the average salary of California registered nurses is not equal to $69,110.

c. Conduct a hypothesis test to determine if the average salary of California registered nurses is less than $69,110.

d. Conduct a hypothesis test to determine if the average salary of California registered nurses is greater than $69,110.

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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.

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