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.
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