This results in a sample mean weight of 837 pounds with a sample standard

This results in a sample mean weight of 837 pounds

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components as they come off the production line. This results in a sample mean weight of 8.37 pounds with a sample standard deviation of .189 pounds. At the .01 level significance, is there enough to support the machine being shut down and recalibrated? List and clearly label all eight steps. Step 1: H 0 : = 8.3 H a : ≠ 8.3 Step 2: t = ´ X ¿ s n ¿ Step 3: α = .01 Step 4: Decision Rule: Reject the Null Hypothesis if t < -2.8609 or if t > 2.8609 Step 5: ´ X = 8.37; s = .189; n = 20; = 8.3 Step 6: t = ´ X ¿ s n ¿ = t = 8.37 - 8.3 .189 20 = 1.6563 Step 7: [-2.8609 ≤ 1.6563 ≤ 2.8609] Therefore we FAIL to Reject the Null Hypothesis. Step 8: At the .01 level of significance, there is not enough evidence to conclude that the machine needs to be shut down and recalibrated.
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HW Problem 39. (5 pts) Suppose a study reports that the average price for a gallon of self-serve regular unleaded gasoline in a particular municipality is $3.16. You believe the figure is higher. With that in mind, you randomly sample 25 gas stations in the municipality which results in a sample mean price of $3.1948 with a sample standard deviation of $.0889. Assume there are 275 gas stations in the municipality. At the .01 level of significance, is the average price higher than $3.16? List and clearly label all eight steps. Step 1: H 0 : = 3.16 H a : > 3.16 Step 2: t = ´ X ¿ ( s n ) ( N n N 1 ) ¿ Step 3: α = .01 Step 4: Decision Rule: Reject the Null Hypothesis if t > 2.4922 Step 5: ´ X = $3.1948; s = $.0889; n = 25; N = 275 = $3.16 Step 6: t = ´ X ¿ ( s n ) ( N n N 1 ) ¿ = 3.1948 3.16 ( .0889 25 ) ( 275 25 275 1 ) = 2.0491 Step 7: [2.0491 is NOT greater than 2.4922] Therefore we FAIL to Reject the Null Hypothesis Step 8: At the .01 level of significance, there is insufficient evidence to conclude that the average price of gasoline is higher than $3.16/gallon.
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