The extrusion length of Twizzles follows a normal distribution with a population

Question

The extrusion length of Twizzles follows a normal distribution with a population standard deviation of 0.250 inches. There is concern that the settings of for the cut to length encoder has changed from a routing software upgrade Historically, the length has always been 15 inches 30 samples were taken at the start of the shift and the average was calculated to be 15.1". Is there sufficient evidence to suggest that the mean cutting length is GREATER than 15 inches? (alpha = 0.05) 1. State the Null Hypothesis State the Alternate 2. State the significance level and one or two tailed 3. State the statistic 4. State the Decision Rule 5. Perform the Calculation - Make the Decision 6. Interpret the result

Explanation / Answer

1) null hypothesis: mean =15

alternate hypothesis: mean>15

2)significance level =0.05

3)statistic : z as we know population std deviation

4)decision rule : reject Ho if z>1.645

5)here std error of mean =std deviation/(n)1/2 =0.0456

hence test stat z=(X-mean)/std error =(15.1-15)/0.0456=2.191

as test stat falls into rejection region , we reject null hypothesis

6) there is sufficient evidence to conclude at 0.05 level that mean cutting length is greater then 15 inches

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