Identify null and alternative hypothesis for testing the difference between two means - independent samples - population standard deviations known

Question

The composition of a quarter dollar coin changed from silver and copper to a copper-nickel alloy in 1964. Hunter Rowland collects coins as a hobby and has access to large collections of quarters produced before and after 1964. He would like to claim that the population mean mass of the quarters produced after 1964 is less than the population mean mass of the quarters produced before 1964. Hunter researches several coin collector websites and assumes the population standard deviation for each type of quarter based on the information gathered from the research. Hunter randomly selects each type of quarter from the large collection and finds the mass of each one using a precise scale. The results of the sampling and the population standard deviations are shown in the table below. Explain whether a hypothesis test for the difference between two means of independent samples is appropriate, and if so, determine the null and alternative hypotheses for this hypothesis test, where

1

is the population mean mass, in grams, of the quarters produced after 1964 and

2

is the population mean mass, in grams, of the quarters produced before 1964.

After 1964Before 1964x

x1=5.648g

n1=37

1=0.070g

x2=6.191g

n2=39

2=0.086g