Question

In: Statistics and Probability

Consider the following hypotheses: H0: σ2 = 210 HA: σ2 ≠ 210 Find the p-value based...

Consider the following hypotheses:

H0: σ2 = 210

HA: σ2 ≠ 210

Find the p-value based on the following sample information, where the sample is drawn from a normally distributed population.

a. s2 = 303; n = 28

b. s2 = 108; n = 28

c. Which of the above sample information enables us to reject the null hypothesis at α = 0.01?

s2 = 303; n = 28

  • Do not reject the null hypothesis  the population variance does not differ from 210.
  • Do not reject the null hypothesis  the population variance differs from 210.
  • Reject the null hypothesis  the population variance differs from 210.
  • Reject the null hypothesis  the population variance does not differ from 210.

s2= 108; n = 28

  • Reject the null hypothesis  the population variance differs from 210.
  • Do not reject the null hypothesis  the population variance differs from 210.
  • Reject the null hypothesis  the population variance does not differ from 210.
  • Do not reject the null hypothesis  the population variance does not differ from 210.

Solutions

Expert Solution

a)

Ho :   σ² =   210
Ha :   σ² ╪   210
      
Level of Significance ,    α =    0.01
sample Variance,   s² =    303
Sample Size ,   n =    28
      
Chi-Square Statistic,   X² = (n-1)s²/σ² =    38.95714286
      
degree of freedom,   DF=n-1 =    27
Two-Tail Test      
Lower Critical Value   =   11.80758735
Upper Critical Value   =   49.6449153
p-Value   =   0.0639
      
  

      

b)

Ho :   σ² =   210
Ha :   σ² ╪   210
      
Level of Significance ,    α =    0.01
sample Variance,   s² =    108
Sample Size ,   n =    28
      
Chi-Square Statistic,   X² = (n-1)s²/σ² =    13.88571429
      
degree of freedom,   DF=n-1 =    27
Two-Tail Test      
Lower Critical Value   =   11.80758735
Upper Critical Value   =   49.6449153
p-Value   =   0.017654548
Ho :   σ² =   210
Ha :   σ² ╪   210
      
Level of Significance ,    α =    0.01
sample Variance,   s² =    108
Sample Size ,   n =    28
      
Chi-Square Statistic,   X² = (n-1)s²/σ² =    13.88571429
      
degree of freedom,   DF=n-1 =    27
Two-Tail Test      
Lower Critical Value   =   11.80758735
Upper Critical Value   =   49.6449153
p-Value   =   0.0177

c)

Do not reject the null hypothesis  the population variance does not differ from 210

D)

Do not reject the null hypothesis  the population variance does not differ from 210

THANKS

revert back for doubt

please upvote


  

orchestra answered 1 year ago
Next > < Previous

Related Solutions

Consider the following hypotheses: H0: σ2 = 210 HA: σ2 ≠ 210 Find the p-value based...
Consider the following hypotheses: H0: σ2 = 210 HA: σ2 ≠ 210 Find the p-value based on the following sample information, where the sample is drawn from a normally distributed population. a. s2= 281; n = 34 The p-value is___________. p-value  0.10 0.05  p-value < 0.10 0.02  p-value < 0.05 0.01  p-value < 0.02 p-value < 0.01 b. s2= 139; n = 34 The p-value is___________. p-value  0.10 0.05  p-value < 0.10 0.02  p-value < 0.05 0.01  p-value < 0.02 p-value < 0.01 c. Which of the above...
Consider the following hypotheses: H0: σ2 = 210 HA: σ2 ≠ 210 Find the p-value based...
Consider the following hypotheses: H0: σ2 = 210 HA: σ2 ≠ 210 Find the p-value based on the following sample information, where the sample is drawn from a normally distributed population. a. s2 = 281; n = 34 p-value  0.10 0.05  p-value < 0.10 0.02  p-value < 0.05 0.01  p-value < 0.02 p-value < 0.01 b. s2 = 139; n = 34 p-value  0.10 0.05  p-value < 0.10 0.02  p-value < 0.05 0.01  p-value < 0.02 p-value < 0.01 c. Which of the above sample information enables us...
Consider the following hypotheses: H0: p ≥ 0.47 HA: p < 0.47 Compute the p-value based...
Consider the following hypotheses: H0: p ≥ 0.47 HA: p < 0.47 Compute the p-value based on the following sample information. (You may find it useful to reference the appropriate table: z tableor t table) (Round "z" value to 2 decimal places. Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.) p-value a. x = 46; n = 121 b. x = 105; n = 269 c. p⎯⎯p¯ = 0.40; n = 62...
Consider the following hypotheses: H0: p ≥ 0.59 HA: p < 0.59 Compute the p-value based...
Consider the following hypotheses: H0: p ≥ 0.59 HA: p < 0.59 Compute the p-value based on the following sample information. (You may find it useful to reference the appropriate table: z table or t table) (Round "z" value to 2 decimal places. Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.) p-value a. x = 44; n = 83 b. x = 135; n = 276 c. p⎯⎯ = 0.55; n =...
Consider the following hypotheses: H0: p ≥ 0.48 HA: p < 0.48 Compute the p-value based...
Consider the following hypotheses: H0: p ≥ 0.48 HA: p < 0.48 Compute the p-value based on the following sample information. (You may find it useful to reference the appropriate table: z table or t table) (Round "z" value to 2 decimal places. Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.) p-value a. x = 50; n = 122 b. x = 118; n = 329 c. p⎯⎯p¯ = 0.42; n =...
Consider the following hypotheses: H0: μ ≤ 520 HA: μ > 520 Find the p-value for...
Consider the following hypotheses: H0: μ ≤ 520 HA: μ > 520 Find the p-value for this test based on the following sample information. a. x¯ = 533; s = 40; n = 19 p-value  0.10 0.05  p-value < 0.10 0.01  p-value < 0.025 0.025  p-value < 0.05 p-value < 0.01 b. x¯ = 533; s = 40; n = 38 0.05  p-value < 0.10 0.01  p-value < 0.025 p-value < 0.01 0.025  p-value < 0.05 p-value  0.10 c. x¯ = 533; s = 32; n = 30...
Consider the following hypotheses: H0: μ ≤ 330 HA: μ > 330 Find the p-value for...
Consider the following hypotheses: H0: μ ≤ 330 HA: μ > 330 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¯ = 340; s = 44; n = 21 p-value  0.10 p-value < 0.01 0.05  p-value < 0.10 0.01  p-value < 0.025 0.025  p-value < 0.05 b. x¯x¯ = 340; s = 44; n = 42 0.01  p-value < 0.025 0.05  p-value < 0.10 0.025  p-value <...
Consider the following hypotheses: H0: μ = 59 HA: μ ≠ 59 Find the p-value for...
Consider the following hypotheses: H0: μ = 59 HA: μ ≠ 59 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¯ = 55; s = 11.4; n = 11 0.01 p-value < 0.02 p-value < 0.01 0.05 p-value < 0.10 p-value 0.10 0.02 p-value < 0.05 b. x¯x¯ = 63; s = 11.4; n = 11 p-value 0.10 0.05 p-value...
Consider the following hypotheses: H0: μ ≤ 370 HA: μ > 370 Find the p-value for...
Consider the following hypotheses: H0: μ ≤ 370 HA: μ > 370 Find the p-value for this test based on the following sample information. a. x⎯⎯x¯ = 380; s = 39; n = 18 b. x⎯⎯x¯ = 380; s = 39; n = 36 c. x⎯⎯x¯ = 380; s = 31; n = 17 d. x⎯⎯x¯ = 377; s = 31; n = 17
Consider the following hypotheses: H0: μ = 42 HA: μ ≠ 42 Find the p-value for...
Consider the following hypotheses: H0: μ = 42 HA: μ ≠ 42 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¯ = 40; s = 10.4; n = 30 0.01 p-value < 0.02 0.02 p-value < 0.05 p-value < 0.01 0.05 p-value < 0.10 p-value 0.10 b. x⎯⎯x¯ = 44; s = 10.4; n = 30 p-value 0.10 0.05 p-value...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT