Question

Exercise 9-39 Algo

Consider the following hypotheses:

H₀: μ = 20
H_A: μ ≠ 20

The population is normally distributed. A sample produces the following observations: (You may find it useful to reference the appropriate table: z table or t table)

24	20	24	21	21	24	19

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a. Find the mean and the standard deviation. (Round your answers to 2 decimal places.)

b. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

c. Find the p-value.

• 0.05 p-value < 0.10
• 0.02 p-value < 0.05
• 0.01 p-value < 0.02

• p-value < 0.01

• p-value 0.10

d. At the 5% significance level, what is the conclusion?

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

• Reject H₀ since the p-value is smaller than α.

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

• Do not reject H₀ since the p-value is smaller than α.

e.  Interpret the results αα = 0.05.

• We conclude that the sample mean differs from 20.

• We cannot conclude that the population mean differs from 20.

• We conclude that the population mean differs from 20.

• We cannot conclude that the sample mean differs from 20.

Answer 1

The statistical software output for this problem is :

Mean = 21.86

standard deviation = 2.12

Test statistics = 2.32

P-value > 0.10

Do not reject H₀ since the p-value is greater than α

We cannot conclude that the sample mean differs from 20.