Question

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 = 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 to reject the null hypothesis at α = 0.01?

s² = 281; n = 34

• 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= 139; n = 34

• 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.

Answer 1

The Null Hypothesis:

The Alternate Hypothesis:

Test statistic used:

where, is the sample size and is the sample variance.

We reject the null hypothesis if p-value > where   is the level of significance.

(a) ;

degrees of freedom = n-1 = 33

p-value is calculated from table

p-value = 0.05 < p-value < 0.10

(b)   ;

degrees of freedom = n-1 = 33

p-value is calculated from table.

p-value > 0.1

(c) , ,  

Here p-value = 0.05 < p-value < 0.10

p-value >

Do not reject the null hypothesis population variance doesnot differ from 210.

(d) , ,

Here, p-value > 0.1

p-value >

Do not reject the null hypothesis population variance doesnot differ from 210.