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snow_lady [41]
3 years ago
15

The sample mean is x = 12.8%. let x be a random variable that represents the percentage of wheat crop in that county lost to hai

l. assume that x has a normal distribution and σ = 5.0%. do these data indicate that the percentage of wheat crop lost to hail in that county is different (either way) from the national mean of 11%? use α = 0.01.
Mathematics
1 answer:
katen-ka-za [31]3 years ago
8 0
Given that \bar{x}=12.8\% and \sigma=5.0\%, given that the population mean is \mu=11\% and the sample size is n = 16, the test statistic is given by

z= \frac{\bar{x}-\mu}{\sigma/\sqrt{n}}  \\  \\ = \frac{12.8-11}{5/\sqrt{16}}  \\  \\ = \frac{1.8}{5/4} = \frac{1.8}{1.25}  \\  \\ =1.44 \\  \\ \Rightarrow p-value=p(z\ \textgreater \ 1.44) \\  \\ =1-P(z\ \textless \ 1.44)=1-0.92507 \\  \\ =0.07493

Since the test is a two tailed test, the p-value is 2(0.07493) = 0.14986

Since the p-value is greater the significant level of α = 0.01, thus, we fail to reject the null hypothesis and conclude that there is no sufficient evidence that <span>the percentage of wheat crop lost to hail in that county is different from the national mean of 11%</span>.
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