Step 1 :Identify the null and alternative hypotheses. The correct null and alternative hypotheses are: \(H_{0}: \sigma=0.16 \mathrm{oz}\) and \(H_{1}: \sigma<0.16 \mathrm{oz}\).
Step 2 :Compute the test statistic. The test statistic is calculated using the formula for the chi-square statistic with the given sample size of 25, sample standard deviation of 0.11 oz, and population standard deviation under the null hypothesis of 0.16 oz. The calculated test statistic is \(\chi^{2}=11.344\).
Step 3 :Find the P-value. The P-value is calculated using the chi-square distribution with 24 degrees of freedom (since the degrees of freedom is n-1). The P-value is the area to the right of the test statistic in the chi-square distribution, since we are testing the alternative hypothesis that the standard deviation is less than 0.16 oz. The calculated P-value is approximately 0.9863.
Step 4 :The final answer is: The correct null and alternative hypotheses are \(H_{0}: \sigma=0.16 \mathrm{oz}\) and \(H_{1}: \sigma<0.16 \mathrm{oz}\). The test statistic is \(\boxed{11.344}\). The P-value is \(\boxed{0.9863}\).