Past data indicate that the variance of measurements made on sheet met

Mary Reyes 2021-12-10 Answered
Past data indicate that the variance of measurements made on sheet metal stampings by experienced quality control inspectors is 0.18 (inch)2. Such measurements made by an inexperienced inspector could have too large a variance (perhaps because of inability to read instruments properly) or too small a variance (perhaps because unusually high or low measurements are discarded). If a new inspector measures 101 stampings with variance of 0.13 (inch)2, test at the 0.05 level of significance whether the inspector is making satisfactory measurements. Assume data is normally distributed.

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Expert Answer

Karen Robbins
Answered 2021-12-11 Author has 4325 answers
Step 1
Hypothesis:
\(\displaystyle{H}_{{{0}}}:\sigma^{{{2}}}={0.18}\)
\(\displaystyle{H}_{{{1}}}:\sigma^{{{2}}}\ne{0.18}\)
Test Statistic \(\displaystyle{\left({X}^{{{2}}}\right)}={\frac{{{\left({n}-{1}\right)}{s}^{{{2}}}}}{{\sigma^{{{2}}}}}}\)
\(\displaystyle={\frac{{{\left({101}-{1}\right)}{\left({0.13}\right)}}}{{{\left({0.18}\right)}}}}\)
\(\displaystyle={72.2222}\)
Thus, the test statistic is 72.2222.
Step 2
P-value is calculated using chi-square test statistic by p-value calculator.
\(\displaystyle{P}-{v}{a}{l}{u}{e}={0.0328096}\)
\(\displaystyle={0.0328}\)
Since P-value is less than 0.05 level of significance, thus there is sufficient evidence to reject the null hypothesis. So \(\displaystyle\sigma^{{{2}}}\ne{0.18}\).
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