Use IDEA to determine the necessary sample size, given the above parameters.

b$.$ Assume that your audit team has decided to increase their reliance on internal control and permit a corresponding increase in the risk of incorrect acceptance from $10$ percent to $15$ percent, which maintains overall audit risk at the same level. What is the necessary sample size, holding all other factors constant?

c$.$ Assume that your audit team has decided to reduce the level of tolerable misstatement from $$311,711$ to $$233,783($or $6$ percent of the recorded balance of the transactions$).$ What is the necessary sample size, holding all other factors constant?

d$.$ Assume that based on additional controls implemented by ELM, your audit team has decided to reduce the expected misstatement from $$77,928$ to $$19,482(0\mathrm{.}5$ percent of the recorded balance of the transactions$).$ What is the necessary sample size, holding all other factors constant?

e$.$ Based on your results in parts $($b$),($c$),$ and $($d$),$ determine the relationship between various parameters and sample size.