Question

N = 9

H0 : 50 = 47
Ha : 50 s = 3
Assume data are from normal population. The p-value is equal to:______.
a. 0.0171.
b. 0.0805.
c. 0.2705.
d. 0.2304.

Answer 1

The p-value is 0.809.

Explanation:

In this case we need to perform a significance test for the standard deviation.

The hypothesis is defined as follows:

H₀: σ₀ = 4 vs. Hₐ: σ₀ ≤ 4

The information provided is:

n = 9

s = 3

Compute the Chi-square test statistic as follows:

`\chi^(2)=((n-1)s^(2))/(\sigma_(0)^(2))`

`=((9-1)\cdot (3)^(2))/((4)^(2))\\\\=(8* 9)/(16)\\\\=4.5`

The test statistic value is 4.5.

The degrees of freedom is:

df = n - 1

= 9 - 1

= 8

Compute the p-value as follows:

`p-value=P(\chi^(2)_(9)>4.5)=0.809`

*Use a Chi-square table.

Thus, the p-value is 0.809.