Suppose that in the town of Springfield, RI, the number of days per year with no measurable precipitation is approximately normally distributed with a mean of 85.1 days and a standard deviation of 7.5 days. Ms. Johnson, who lives on a farm just outside of Springfield, wonders if the mean number of days with no measurable precipitation on her farm is different from in town. Her grandfather maintained meticulous weather records. She obtains a simple random sample of eight years from her grandfather's records, and determines that the mean number of days with no measurable precipitation in those years was 82.3 days. She plans to conduct a one-sample? z ‑test, assuming that the standard deviation of days with no measurable precipitation is the same at the farm as in town. Choose the appropriate null and alternative hypotheses for such a test.

Question

Andreas Keith

Mathematics

12 February, 06:35

Suppose that in the town of Springfield, RI, the number of days per year with no measurable precipitation is approximately normally distributed with a mean of 85.1 days and a standard deviation of 7.5 days. Ms. Johnson, who lives on a farm just outside of Springfield, wonders if the mean number of days with no measurable precipitation on her farm is different from in town. Her grandfather maintained meticulous weather records. She obtains a simple random sample of eight years from her grandfather's records, and determines that the mean number of days with no measurable precipitation in those years was 82.3 days. She plans to conduct a one-sample? z ‑test, assuming that the standard deviation of days with no measurable precipitation is the same at the farm as in town. Choose the appropriate null and alternative hypotheses for such a test.

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Answers (1)

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Samir · Answer 1

H0: µ = 85.1

Ha: µ ≠ 85.1

Step-by-step explanation:

She wants to see if the number of days is different. It could be higher or lower, so the alternate hypothesis uses the "not equal to" sign. If she wanted to see if it rained more on the farm, her alternate hypothesis would be

Ha: µ > 85.1

If she wanted to see if it rained less, then she would use the alternate hypothesis of Ha: µ < 85.1