The Weather Underground reported that the mean amount of summer rainfall for the northeastern US is at least 11.52 inches. Ten cities in the northeast are randomly selected and the mean rainfall amount is calculated to be 7.71 inches with a standard deviation of 1.3 inches. At the α = 0.05 level, can it be concluded that the mean rainfall was below the reported average? Assume the amount of summer rainfall follows a normal distribution. a) What can be said about the p-value for the test? p-value > 0.100 0.050 < p-value < 0.100 0.025 < p-value < 0.050 0.010 < p-value < 0.025 0.005 < p-value < 0.010 p-value < 0.005 b) State Alpha.
Added by Stephanie M.
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71 inches - Population mean (\( \mu \)) = 11.52 inches - Sample standard deviation (s) = 1.3 inches - Sample size (n) = 10 \[ t = \frac{7.71 - 11.52}{1.3/\sqrt{10}} \] \[ t = \frac{-3.81}{1.3/3.162} \] \[ t = \frac{-3.81}{0.411} \] \[ t = -9.268 \] ** Show more…
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The Weather Underground reported that the mean amount of summer rainfall for the northeastern US is at least 11.52 inches. Ten cities in the northeast are randomly selected and the mean rainfall amount is calculated to be 7.42 inches with a standard deviation of 1.3 inches. At the $\alpha=0.05$ level, can it be concluded that the mean rainfall was below the reported average? What if $\alpha=0.01 ?$ Assume the amount of summer rainfall follows a normal distribution.
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