SOLUTION: Problem 10-36. The Rutter Nursery Company packages their pine bark mulch in 50-pound bags. From a long history, the production department reports that the distribution of the bag

Question 143676This question is from textbook Statistical Techniques in business and economics
: Problem 10-36. The Rutter Nursery Company packages their pine bark mulch in 50-pound bags. From a long history, the production department reports that the distribution of the bag weights follows the normal distribution and the standard deviation of this processis 3 pounds per bag. At the end of each day, Jeff Rutter, the production manager, weighs 10 bags and computes the mean weight of the sample. Below are the weights of 10 bags from today's production.
45.6 47.7 47.6 46.3 46.2 47.4 49.2 55.8 47.5 48.5
a. Can Mr. Rutter conclude that the mean weight of the bags is less than 50 pounds? Use the .01 significance level.
b. In a brief report, tell why Mr. Rutter can use the z distribution as the test statistic.
c. Compute the p-value.
This question is from textbook Statistical Techniques in business and economics

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The Rutter Nursery Company packages their pine bark mulch in 50-pound bags. From a long history, the production department reports that the distribution of the bag weights follows the normal distribution and the standard deviation of this processis 3 pounds per bag. At the end of each day, Jeff Rutter, the production manager, weighs 10 bags and computes the mean weight of the sample. Below are the weights of 10 bags from today's production.
45.6 47.7 47.6 46.3 46.2 47.4 49.2 55.8 47.5 48.5
x-bar=48.18 ; s=2.886
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a. Can Mr. Rutter conclude that the mean weight of the bags is less than 50 pounds? Use the .01 significance level.
Ho: u = 50
Ha: u < 50
z(48.18) = (48.18-50)/[3/sqrt(10)] = -1.91845...
p-value: P(-10 < z < -1.91845) = 0.02753
Since p-value is greater than 1%, fail to reject Ho.
The mean is statistically equal to 50 lbs.
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b. In a brief report, tell why Mr. Rutter can use the z distribution as the test statistic.
I'll leave that to you as the reasons differ in various texts.
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c. Compute the p-value.
Done above
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Cheers,
Stan H.

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