Question

please help and explain steps, thank you very much!

Reginald Brown, an inspector from the Department of Weights and Measures, weighs 15 eighteen-ounce cereal boxes of corn flakes. He finds their mean weight to be 17.78 ounces with a standard deviation of 0.4 ounces. At the.01 level of significance, does this sample data provide evidence that the the cereal boxes lighter than they should be? I.e., is there significant evidence that the mean weight of the boxes is less than 18 ounces?

Answer 1

Step 1:

Ho : $\mu$ = 18

Ha:  $\mu$ < 18

Step 2: Test statistics

n = 15

sample mean = 17.78

sample sd = 0.4

Assuming that the data is normally distributed and as the population sd is not given, we will use t stat

$t = \frac{\bar{x}- \mu}{s/\sqrt{n}} =\frac{ 17.78 - 18 }{0.4/ \sqrt{15}}$

t = -2.130

Step 3:

df = 14

alpha = 0.01

t criical for left tailed test = - 2.62449407

As t stat (-2.130) does not fall in the rejection area, we fail to reject the Null hypothesis.

Hence we do not have sufficient evidence to believe that the mean weight of the boxes is less than 18 ounces.