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.

Question

Dominick

Mathematics

20 February, 08:44

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.

+4

Answers (1)

Know the Answer?

Barton · Answer 1

the pennies does not conform to the US mints specification

Step-by-step explanation:

z = (variate - mean) / standard deviation

z = 2.5 - 2.4991 / 0.01648 = 0.0546

we 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 > 0.05claim

since 0.4781 > 0.05claim, therefore, the pennies does not conform to the US mints specification

the claim state a 5% significance level whereas the calculated significance level is 47.81%. therefore, the claim should be rejected