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Chapter 9: Q. 112 (page 555)

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 α=0.05 level, can it be concluded that the mean rainfall was below the reported average? What if α=0.01? Assume the amount of summer rainfall follows a normal distribution.

Short Answer

Expert verified

There is sufficient evidence to conclude that mean rainfall was below the reported average11.52inches.

Step by step solution

01

Given information

M=7.42inches,S=1.3inches,n=10.

02

Explanation

State the hypothesis:

The null hypothesis states that mean rainfall is greater than or equal to the reported average 11.52inches. In symbols:

H0:μ≥11.52

The alternative hypothesis states that mean rainfall is less than the reported average 11.52inches. In symbols:

Ha:μ<11.52

The degree of freedom is:

df=n-1=10-1=9

The test statistic is:

t=M-μS/n=7.42-11.521.3/10=-4.100.4111=-9.97

The p-valueis0.0000

Since p-value<0.05and p-value<0.01also, reject the null hypothesis at a=0.05anda=0.01both. We conclude that mean rainfall is less than the reported average 11.52inches.

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