Question

A scrap metal dealer claims that the mean of his cash scales is "no more than $80," but an Internal Revenue Service agent believes the dealer is truthful. Observing a sample of 20 cash customers, the agent finds the mean purchases to be $91, with a standard deviation of $21. Assuming the population is approximately normally distributed, and using the 0.05 level of significance, what is the calculated value of test statistic

Answer 1

Answer: 2.3425

Step-by-step explanation:

As per given , we have

$\mu=80$

n = 20

$\overline{x}=91\\\\ s=21$

We assume that the population is approximately normally distributed.

Since population standard deviation is unknown , so we use t-test.

Test statistic : $t=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

$\\\\ t=\dfrac{91-80}{\dfrac{21}{\sqrt{20}}}=2.342547405\approx2.3425$

Hence, the calculated value of test statistic = 2.3425