Step 1 :The null hypothesis (H0) is that the standard deviation is equal to 0.14 oz, and the alternative hypothesis (H1) is that the standard deviation is less than 0.14 oz.
Step 2 :The test statistic can be computed using the formula for the chi-square statistic: \(\chi^{2} = \frac{(n-1)s^{2}}{\sigma^{2}}\), where n is the sample size, s is the sample standard deviation, and \(\sigma\) is the standard deviation under the null hypothesis.
Step 3 :Substitute the given values into the formula: \(\chi^{2} = \frac{(20-1)(0.11)^{2}}{(0.14)^{2}}\)
Step 4 :Simplify the equation: \(\chi^{2} = \frac{19*0.0121}{0.0196}\)
Step 5 :Calculate the test statistic: \(\chi^{2} = 11.76\)
Step 6 :So, the test statistic is \(\boxed{11.76}\) (rounded to two decimal places).