An environmentalist estimates that the mean waste recycled by adults is more than $1$ pound per day. You want to test this claim. You find that the mean waste recycled per person per day for a random sample of $8$ adults in the country is $1\mathrm{.}1$ pounds and the standard deviation of the population is $0\mathrm{.}2$ pounds. At $=0\mathrm{.}05,$ can you support this claim? Assume the population is normally distributed.

a$)$ State the claim as a mathematical statement

b$)$ State the null hypothesis $H_0$

c$)$ State the alternate hypothesis $H_a$

d$)$ State the test statistic

e$)$ Do you reject $H_o$ or fail to reject $H_0?$

f$)$ Can you support the claim?