Question

Consider the following hypotheses:

H₀: μ ≤ 270

H_A: μ > 270

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¯ = 277; s = 23; n = 18

• 0.025   p-value < 0.05
• 0.01   p-value < 0.025
• p-value    0.10
• 0.05   p-value < 0.10

• p-value < 0.01

b. x¯x¯ = 277; s = 23; n = 36

• p-value   0.10
• 0.025   p-value < 0.05
• 0.05   p-value < 0.10

• p-value < 0.01

• 0.01   p-value < 0.025

c. x¯x¯ = 277; s = 14; n = 11

• 0.05   p-value < 0.10
• p-value   0.10

• p-value < 0.01

• 0.01   p-value < 0.025

• 0.025   p-value < 0.05

d. x¯x¯ = 275; s = 14; n = 11

• 0.01   p-value < 0.025

• p-value < 0.01

• p-value   0.10
• 0.05    p-value < 0.10
• 0.025   p-value < 0.05

Answer 1

Date: 11/11/2019 Answer The null and alternative hypothesis is, Ho u 270 Hu270 a a) The f-test statistics is, t= /Jn 277 270 23//18 = 2.284 The f-test statistics is 2.284 The p-value for this test is, From the t distribution table, show the degree of freedom is,

d.f. n-1 =18 -1 17 and f-test statistics is 2.284 and the p-value is between 0.01 and 0.025. The p-value for this test is 0.01 < P < 0.025 b) The f-test statistics is, t s/n 277 270 = 23//36 -3.231 The f-test statistics is 3.231. The p-value for this test is

From the t distribution table, show the degree of freedom is, d.f. n- - 36 -1 35 and f-test statistics is 3.231 and the p-value is less than 0.01 గ The p-value for this test is 0.01 c) The f-test statistics is, t= s/n 277 270 14//11 1.658 The f-test statistics is 1.658

The p-value for this test is, From the f distribution table, show the degree of freedom is, d.f.- n-1 11-1 10 and f-test statistics is 1.658 and the p-value is between less than or equal 0.05 and 0.10 ww The p-value for this test is 0.05 <p<0.10 d) The f-test statistics is, t = $/n 275 270 14//11 -1.185

The f-test statistics is 1.185 The p-value for this test is, From the t distribution table, show the degree of freedom is, d.f. n-1 11-1 =10 and f-test statistics is 1.185 and the p-value is greater than or equal 0.10. ww The p-value for this test is 20.10