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a manufacturer must test that his bolts are 1.00cm long when they come off the assembly line. he must recalibrate 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 1.06cm. he knows that the population standard deviation is 0.22cm. assuming a level of significance of 0.10, 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.

Sagot :

p < 0.10, there is sufficient evidence to conclude that the machines' maker should perform a recalibration.

In this question we have,

The population mean μ = 1.00

The sample size n = 49

The sample mean X = 1.06

The standard deviation σ = 0.22cm

The significance level α = 0.10

So, the hypothesis is:

The null hypothesis: H0: μ = 1

The alternative hypothesis: Ha: μ ≠ 1

Thus, the test statistic value is,

z = (X - μ)/(σ/√n)

= (1.06 - 1)/(0.22/√49)

= 0.06 / 0.03142

= 1.91

So, for z = 1.91, the p-value is 0.028067.

The provided significance level of 0.10 is not met by the p-value of (0.028067).

Therefore, there is enough evidence to support the claim that the machines' manufacturer needs to recalibrate them.

Learn more about significance level here:

brainly.com/question/28041970

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