An expert at the Icelandic Meteorological Office is tasked with investigating whether the air quality in the capital area is in accordance with health protection limits. According to them, dust particles should not amount to more than 50 micrograms per cubic meter. The expert collects readings from around the town between 9 and 10 in the morning a. State and perform a one-sided hypothesis test (at a 2% level of significance) about whether the population mean is greater than 50 micrograms. NOTE that the Norwegian Meteorological Agency assumes that the air quality is acceptable unless there is strong evidence that this is not the case. b. Show the result of the test in a picture. What does the result tell you about the sampling distribution of the sample mean? c. What is the p-value and what does it tell you? Show it in the picture you made in part b d. Draw the power function of the hypothesis test e. The measuring devices that are used to measure air quality can be problematic, so the Norwegian Meteorological Agency's technicians have set up a system to know when the condition of the equipment needs to be checked. If the variance of the measurements is over 3000 acc. a hypothesis test with a 5% significance level, the condition of the equipment is examined. Present this hypothesis test and calculate its result. NOTE that the technicians assume that the equipment is fine unless there are strong signs that this is not the case.
An expert at the Icelandic Meteorological Office is tasked with investigating whether the air quality in the capital area is in accordance with health protection limits. According to them, dust particles should not amount to more than 50 micrograms per cubic meter. The expert collects readings from around the town between 9 and 10 in the morning
a. State and perform a one-sided hypothesis test (at a 2% level of significance) about whether the population mean is greater than 50 micrograms. NOTE that the Norwegian Meteorological Agency assumes that the air quality is acceptable unless there is strong evidence that this is not the case.
b. Show the result of the test in a picture. What does the result tell you about the sampling distribution of the sample mean?
c. What is the p-value and what does it tell you? Show it in the picture you made in part b
d. Draw the power
e. The measuring devices that are used to measure air quality can be problematic, so the Norwegian Meteorological Agency's technicians have set up a system to know when the condition of the equipment needs to be checked. If the variance of the measurements is over 3000 acc. a hypothesis test with a 5% significance level, the condition of the equipment is examined. Present this hypothesis test and calculate its result. NOTE that the technicians assume that the equipment is fine unless there are strong signs that this is not the case.
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