Question

Consider the following hypotheses:

H₀: μ ≤ 210

H_A: μ > 210

Find the p-value for this test based on the following sample information. (You may find it useful to reference the appropriate table: z table or t table)

a. x⎯⎯x¯ = 216; s = 26; n = 40

• p-value < 0.01

• 0.01 ≤ p-value < 0.025

• 0.025 ≤ p-value < 0.05

• 0.05 ≤ p-value < 0.10

• p-value ≥ 0.10

b. x⎯⎯x¯ = 216; s = 26; n = 80

• p-value < 0.01

• 0.01 ≤ p-value < 0.025

• 0.025 ≤ p-value < 0.05

• 0.05 ≤ p-value < 0.10

• p-value ≥ 0.10

c. x⎯⎯x¯ = 216; s = 16; n = 40

• p-value < 0.01

• 0.01 ≤ p-value < 0.025

• 0.025 ≤ p-value < 0.05

• 0.05 ≤ p-value < 0.10

• p-value ≥ 0.10

d. x⎯⎯x¯ = 214; s = 16; n = 40

• p-value < 0.01

• 0.01 ≤ p-value < 0.025

• 0.025 ≤ p-value < 0.05

• 0.05 ≤ p-value < 0.10

• p-value ≥ 0.10

Answer 1

The statistical software output for this problem is :

(a)

One sample T summary hypothesis test: u Mean of population HO:u=210 HA1 > 210 Hypothesis test results: Mean Sample Mean Std. Err. DF T-Stat P-value 216 4.110961 39 1.4595128 0.0762

0.05 ≤ p-value < 0.10

(b)

One sample T summary hypothesis test: u Mean of population Ho:u=210 HA: > 210 Hypothesis test results: Mean Sample Mean Std. Err. DF T-Stat 216 2.9068884 79 2.0640627 P-value 0.0211

0.01 ≤ p-value < 0.025

(c)

One sample T summary hypothesis test: u Mean of population Ho:u=210 Hu> 210 Hypothesis test results: Mean Sample Mean Std. Err. DF T-Stat 216 2.5298221 39 2.3717082 P-value 0.0114

0.01 ≤ p-value < 0.025

(d)

One sample T summary hypothesis test: u Mean of population HO:u=210 HA!u> 210 Hypothesis test results: Mean Sample Mean Std. Err. DFT-Stat 214 2.5298221 39 1.5811388 P-value 0.061

0.05 ≤ p-value < 0.10