A manufacturer of a pasta sauce claims that there 471mg of sodium in a half-cup (125mL) of the sauce. To test this claim, a random sample 23 jars of pasta sauce are analyzed and a mean of 498.78mg of sodium is found with a standard deviation of 46.94mg. Assume the amount of sodium follows a normal distribution.
-The appropriate test statistic to test the hypotheses is _____.
A)2.84
B)13.61
C)30.34
D)-2.84
E)-13.61

Question

Quizplus · Accepted Answer

The test statistic is calculated using the formula $z = \frac{\bar{x} - \mu}{(\sigma/\sqrt{n})}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $\sigma$ is the standard deviation, and $n$ is the sample size. Plugging in the given values: $z = \frac{498.78 - 471}{(46.94/\sqrt{23})}$ results in a z-value of approximately 2.84, indicating option A is correct.

A Manufacturer of a Pasta Sauce Claims That There 471mg