Suppose a brand of recycled shingles is advertised to weigh 185 pounds per squar

Question

Suppose a brand of recycled shingles is advertised to weigh 185 pounds per square foot. A random sample of these shingles was obtained, and the weight of each is given in the following table. Assume the underlying population is normal and that sigma = 2.7. Is there any evidence to suggest that the true mean weight of these recycled is greater than 185 pounds per square foot? Compute the p-value and compare it to alpha = 0.01 to draw your conclusion. (You can use ZTEST to compute p, but that will result in reduced credit).

Explanation / Answer

Here,

Null Hypothesis : H0 : = 185 pounds per square feet

Alternative Hypothesis : Ha : > 185 pounds per square feet

Mean of the given sample xbar = xi /n = 185.73 pounds per square feet

Standard deviation of the sample s = sqrt (xi -xbar )2 /(n-1) = 1.9658

as population standard deviation is given, we will use population deviation to calculate standard error of the mean of the sample and use Z - test for hypothesis testing.

standard error of the mean of the sample se0 = /n = 2.7/20 = 0.6037

so test statistic

Z = (xbar -  H)/ se0 = (185.73 - 185)/ 0.6037 = 1.21

P- value = Pr( xbar > 185.73; 185; 0.6037) = 1- (1.21)

where is the cumulative normal standard probability distribution

p - value = 1- 0.8869 = 0.1131

so p - value > alpha = 0.01 so it is not under significance level so we cannot reject the null hypothesis and can conclude that true mean weight of these recycled shingles is equal to 185 pounds per square feet.

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