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a manufacturer must test that his bolts are 5.00cm long when they come off the assembly line. he must calibrate his machines if the bolts are too long or too short. after sampling 49 randomly selected bolts off the assembly line, he calculates the sample mean to be 4.88cm. he knows that the population standard deviation is 0.44cm. assuming a level of significance of 0.01, is there sufficient evidence to show that the manufacturer needs to recalibrate the machines? step 2 of 3 : compute the value of the test statistic. round your answer to two decimal places.

Respuesta :

Given that the test's p-value is 0.0562>0.05, there is enough data to conclude that the machines' manufacturer should perform a new calibration.

What is test statistic?

A statistic employed in statistical hypothesis testing is known as a test statistic. A test statistic, which can be thought of as a numerical summary of a data set that condenses the data into a single value that can be used to conduct the hypothesis test, is how a hypothesis test is commonly expressed.

Here,

x=4.88 cm

μ=5 cm

σ=0.44 cm

n=49

The test statistic,

=(4.88-5)/(0.44/7)

z=-1.909

The p-value of the test is the probability that the sample mean is different by at least 4.88 - 5 = 0.12 from the target value, which is P(|z| > -1.909), which is 2 multiplied by the p-value of z = -1.909

At z=-1.909, p-value=0.0281

2*0.0281=0.0562

The test's p-value is 0.0562>0.05, indicating that there is enough data to conclude that the machines' manufacturer should perform a recalibration.

To know more about test statistic,

https://brainly.com/question/23161548

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