A company has a contract to supply specialized batteries to a manufacturer with a mean width of 54mm and a standard deviation of 1.5 or less with an alpha of 0.10.The company randomly tests 25 of these batteries to ensure that they are meeting the requirements of the contract.If the most recent test had a standard deviation of 1.8 what would be the critical value of this chi-squared test?
A)-33.196
B)36.415
C)1.645
D)33.196
E)1.282

Question

Quizplus · Accepted Answer

The critical value for a chi-squared test with $n - 1$ degrees of freedom (where $n$ is the sample size) and a significance level ($\alpha$) of 0.10 (for a two-tailed test, but in this context, we're likely looking at a one-tailed test since we're concerned with whether the standard deviation exceeds a certain threshold, not if it's simply different) can be found using chi-squared distribution tables or software. For a sample size of 25, the degrees of freedom ($df$) would be $25 - 1 = 24$. Looking up the critical value for $df = 24$ and $\alpha = 0.10$ (one-tailed) in a chi-squared distribution table or using software gives us a critical value close to 33.196.

A Company Has a Contract to Supply Specialized Batteries to a Manufacturer