Question

# Exercise 9-40 Algo Consider the following hypotheses: H0: μ ≥ 160 HA: μ < 160 The...

Exercise 9-40 Algo

Consider the following hypotheses:

H0: μ ≥ 160
HA: μ < 160

The population is normally distributed. A sample produces the following observations:

 160 142 152 159 158 140

Conduct the test at the 5% level of significance. (You may find it useful to reference the appropriate table: z table or t table)

a. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

b. Find the p-value.

• 0.025 p-value < 0.05
• 0.01 p-value < 0.025
• p-value < 0.01

• p-value 0.10
• 0.05 p-value < 0.10

c. What is the conclusion?

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

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

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

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

d. Interpret the results   αα = 0.05.

• We cannot conclude that the population mean is less than 160.

• We conclude that the population mean is less than 160.

• We cannot conclude that the population mean is greater than 160.

• We conclude that the population mean is greater than 160. 