Question

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 121 randomly selected bolts off the assembly line, he calculates the sample mean to be 0.94cm. he knows that the population standard deviation is 0.31cm. assuming a level of significance of 0.05, is there sufficient evidence to show that the manufacturer needs to recalibrate the machines?

Answer 1

There is insufficient evidence to support that bolts are too long or too short.

What is Mean and Standard Deviation?

Mean: Dividing the sum of all values in a data set by the number of values.

Standard Deviation: The standard deviation is a measure that summarizes how far away from the mean each observation is.

Given:

mean: 0.94cm

standard deviation = 0.31cm

Alright, so a manufacturer must test that these bolts are long as they come off the manufacturing line and he must readjust the machines if they're too long or too short. Consequently, sample 121V and sample mean are 0.94 cm. So we want to test whether or not these are actually equal to two, so are no hypothesis is that the mean is too and our alternative hypothesis, because it says that we have to recalibrate if they're too short or too long, is that the mean is not too we could probably go with the left tail test here because the sample mean is under but we'll be safer with a two tail test um just because the standard deviation may sway things.

So what we want to do next is compute the test statistic and that's gonna be a Z score and that's just supplied by X bar minus population mean over standard deviation over squared event. And we're using Z here because we have a high sample size and since we know the population standard deviation.

Hence, There is insufficient evidence to support that bolts are too long or too short.

To know more about Mean and Standard Deviation visit,

brainly.com/question/475676

#SPJ4