The Food and Drug Administration (FDA) regulates the amount of mercury in consumable fish, where consumable fish should only contain at most $1 \mathrm{mg} / \mathrm{kg}$ of mercury. In Florida, bass fish were collected in 50 different lakes to measure the amount of mercury in the fish from each of the 50 lakes. Do the data provide enough evidence to show that the fish in all Florida lakes have lower mercury than the allowable amount? State the random variable, population parameter, and hypotheses. a. The symbol for the random variable involved in this problem is ? b. The wording for the random varfable in context is as follows: Select an answer c. The symbol for the parameter involved in this problem is ?V d. The wording for the parameter in context is as follows: Select an answer e. Fill in the correct null and alternative hypotheses. \[ \begin{array}{l} H_{0}: ? v[?] \\ H_{A}: ? v[? v \end{array} \] f. A Type / error in the context of this problem would be Select an answer g. A Type II error in the context of this problem would be Select an answer

Step 1 ：The problem is a hypothesis testing problem. We are trying to determine if the mean amount of mercury in fish from all Florida lakes is less than the FDA allowable amount of 1 mg/kg.

Step 2 ：The random variable in this problem is the amount of mercury in a randomly selected fish from a Florida lake.

Step 3 ：The population parameter is the mean amount of mercury in all fish from all Florida lakes.

Step 4 ：The null hypothesis is that the mean amount of mercury in all fish from all Florida lakes is equal to the FDA allowable amount of 1 mg/kg.

Step 5 ：The alternative hypothesis is that the mean amount of mercury in all fish from all Florida lakes is less than the FDA allowable amount of 1 mg/kg.

Step 6 ：A Type I error would occur if we reject the null hypothesis when it is true, meaning we conclude that the mean amount of mercury in all fish from all Florida lakes is less than the FDA allowable amount when it is actually equal to it.

Step 7 ：A Type II error would occur if we fail to reject the null hypothesis when it is false, meaning we conclude that the mean amount of mercury in all fish from all Florida lakes is equal to the FDA allowable amount when it is actually less than it.

Step 8 ：The symbol for the random variable involved in this problem is X.

Step 9 ：The wording for the random variable in context is 'the amount of mercury in a randomly selected fish from a Florida lake'.

Step 10 ：The symbol for the parameter involved in this problem is \(\mu\).

Step 11 ：The wording for the parameter in context is 'the mean amount of mercury in all fish from all Florida lakes'.

Step 12 ：The null and alternative hypotheses are: \[\begin{array}{l} H_{0}: \mu = 1 \\ H_{A}: \mu < 1 \end{array}\]

Step 13 ：A Type I error in the context of this problem would be 'concluding that the mean amount of mercury in all fish from all Florida lakes is less than the FDA allowable amount when it is actually equal to it'.

Step 14 ：A Type II error in the context of this problem would be 'concluding that the mean amount of mercury in all fish from all Florida lakes is equal to the FDA allowable amount when it is actually less than it'.