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You decide to test how accurate a certain TV station's weatherman is with his predictions. Over the course of several months, you note that there were 40 days where the weatherman said that there was a 60% chance of rain. It subsequently rained on 21 of those days. Evaluate the weathermans forecasting ability on the basis of this data The p-value of the hypothesis test is:______

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Answer:

0.483

Step-by-step explanation:

Given that you decide to test how accurate a certain TV station's weatherman is with his predictions.

No of days = 40

weatherman prediction of proportion= 0.60

Observed proportion = [tex]\frac{21}{40} =0.525[/tex]

p difference = -0.075

[tex]H_0: p = 0.60\\H_a: p \neq 0.60[/tex]

(Two tailed test)

Assuming H0 to be true, std error = [tex]\sqrt{\frac{pq}{n} } \\=0.1069[/tex]

Test statistic Z = p difference/std error

= -0.7016

p value = 0.483