Question

N = 9

Answer 1

Answer:

The p-value is 0.809.

Step-by-step 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:

$\chi^{2}=\frac{(n-1)s^{2}}{\sigma_{0}^{2}}$

     $=\frac{(9-1)\cdot (3)^{2}}{(4)^{2}}\\\\=\frac{8\times 9}{16}\\\\=4.5$

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.