Question

Suppose that an independent research company was tasked with testing the validity of complaints against a pesticide manufacturing firm for under-filling their 20 lb bags of pesticide. Past experience has shown that the amount of pesticide dispensed by the machines that fill the bags follows a normal distribution with a mean of 20 lb and a standard deviation of 0.6 lb. To verify the validity of the complaints, a researcher randomly selected 16 of the firm's 20 lb pesticide bags and recorded the following weights. 18.59, 19.74, 19.18, 20.09, 18.54, 20, 19.04, 19.24, 19.23, 20.31, 19.74, 18.69, 18.61, 20.18, 18.68, 20.28 If you wish, you may download the data in your preferred format. CrunchIt! CSV Excel JMP Mac Text Minitab PC Text R SPSS TI Calc The mean weight of the 16 bags collected was 19.384 lb. Calculate the value of the one-sample z- statistic. Give your answer precise to three decimal places.

Answer 1

Here $\mu=20$, $\sigma=0.6$, n=16 and $\overline{x}=19.384$

So test statistics is $z=\frac{\overline{x}-\mu}{\frac{\sigma }{\sqrt{n}}}=\frac{19.384-20}{\frac{0.6}{4}}=-4.107$