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Statistics and Probability

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Moderate

Null and Alternative Hypotheses about Annual Incomes

STATS-ECKVPE

The mean gross annual income of certified nurses are normally distributed with the mean of $\$50,000$ and a standard deviation of $\$6,000$. The nurse association wishes to find out whether their nurses earn more or less than $\$50,000$ annually.

A random sample of $400$ certified nurses was surveyed. The sample mean of these nurses' annual income is $\$56,000$ with a standard deviation of $\$7,000$.

Which of the following is the alternative hypothesis?

A

Alternate: $µ > \$50,000$

B

Alternate: $µ < \$50,000$

C

Alternate: $µ ≠ \$50,000$

D

Alternate: $µ ≠ \$56,000$