Step 1 :The null hypothesis is \(H_{0} : \sigma = 0.007\).
Step 2 :The alternative hypothesis is \(H_{1} : \sigma < 0.007\).
Step 3 :The value of the test statistic is calculated as \(\chi^{2} = (n - 1)\frac{s^{2}}{\sigma^{2}} = (23 - 1)\frac{0.0051^{2}}{0.007^{2}} = 11.678\).
Step 4 :The P-value is calculated using a chi-square distribution with degrees of freedom equal to the sample size minus 1, which gives a P-value of 0.964.
Step 5 :Since the P-value is greater than the level of significance (0.05), we fail to reject the null hypothesis.
Step 6 :There is not sufficient evidence to conclude that the standard deviation has decreased at the 0.05 level of significance.