Consider the following hypotheses:

H₀: μ = 380
H_A: μ ≠ 380

The population is normally distributed with a population standarddeviation of 77. (You may find it useful to reference theappropriate table: z table or ttable)

a-1. Calculate the value of the test statisticwith x−x− = 390 and n = 45. (Round intermediatecalculations to at least 4 decimal places and final answer to 2decimal places.)

a-2. What is the conclusion at the 10%significance level?

• Reject H₀ since the p-value is lessthan the significance level.

• Reject H₀ since the p-value isgreater than the significance level.

• Do not reject H₀ since the p-valueis less than the significance level.

• Do not reject H₀ since the p-valueis greater than the significance level.

a-3. Interpret the results at αα = 0.10.

• We conclude that the population mean differs from 380.

• We cannot conclude that the population mean differs from380.

• We conclude that the sample mean differs from 380.

• We cannot conclude that the sample mean differs from 380.

b-1. Calculate the value of the test statisticwith x−x− = 345 and n = 45. (Negative value shouldbe indicated by a minus sign. Round intermediate calculations to atleast 4 decimal places and final answer to 2 decimalplaces.)

b-2. What is the conclusion at the 5% significancelevel?

• Reject H₀ since the p-value isgreater than the significance level.

• Reject H₀ since the p-value is lessthan the significance level.

• Do not reject H₀ since the p-valueis greater than the significance level.

• Do not reject H₀ since the p-valueis less than the significance level.

b-3. Interpret the results at αα = 0.05.

• We conclude that the population mean differs from 380.

• We cannot conclude that the population mean differs from380.

• We conclude that the sample mean differs from 380.

• We cannot conclude that the sample mean differs from 380.