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

Consider the following hypotheses:

H₀: σ² = 210

H_A: 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

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

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

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

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