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

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 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

Answer: Consider the following hypotheses:

H0: σ^2 = 210

HA: σ^2 ≠ 210

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

Solution:

a. s^2= 281; n = 34

Using Chi square test statistic χ2:

χ2 = (n-1)s^2/σ^2

χ2 = (34-1)281/210

χ2 = 44.1571

P-value:

df = n-1 = 34-1 =33

P-value = 0.0928

0.05 < p-value < 0.10

b. s^2= 139; n = 34

Using Chi square test statistic χ2:

χ2 = (n-1)s^2/σ^2

χ2 = (34-1)139/210

χ2 = 21.8428

P-value:

df = n-1 = 34-1 =33

P-value = 0 .93104

p-value > 0.10

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

s^2= 281; n = 34

Since P-value (0.0928) > α (0.01) significance level.

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

s^2= 139; n = 34

Since P-value (0.9310) > α (0.01) significance level.

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