A psychologist has designed a new intelligence test. Historically, time to complete the old test was an average of 120 minutes. With the altered format of the test, the psychologist claims that the time to complete the test is no longer 120 minutes. A sample of 50 new test taking times yielded an average time of 118 minutes. The population standard deviation is known to be 5 minutes
-The test statistic to test these hypotheses is _____.
A)-2.83
B)-6.32
C)5.64
D)-5.64
E)2.82

Question

Quizplus · Accepted Answer

The test statistic for this hypothesis testing scenario is calculated using the formula for a z-test, given that the population standard deviation is known. The formula is $z = \frac{\bar{x} - \mu}{(\sigma / \sqrt{n})}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the given values ($\bar{x} = 118$, $\mu = 120$, $\sigma = 5$, $n = 50$), we get $z = \frac{118 - 120}{(5 / \sqrt{50})} = -2.83$.

A Psychologist Has Designed a New Intelligence Test