1. The US Mint has a specification that pennies have a mean weight of 2.5g. From a sample of 37 pennies, the mean weight is found to be 2.49910g. and the standard deviation is found to be 0.01648g. Use a 0.05 significance level to test the claim that this sample is from a population with a mean weight equal to 2.5g. Do the pennies appear to conform to the specifications of the US Mint? The data can be found in the CoinWeights.mtw file on Blackboard.

Answer:the pennies does not conform to the US mints specificationStep-by-step explanation:z = (variate -mean)/ standard deviationz= 2.5 - 2.4991 / 0.01648 = 0.0546we are going to check the value of z in the normal distribution table, which is the table bounded by z.checking for z= 0.0 under 55 gives 0.0219 (value gotten from the table of normal distribution)we subtract the value of z from 0.5 (1- (0.5+0.0219)) = 0.4781 > 0.05claimsince 0.4781 > 0.05claim, therefore, the pennies does not conform to the US mints specificationthe claim state a 5% significance level whereas the calculated significance level is 47.81%. therefore, the claim should be rejected