Question

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 427 gram setting. It is believed that the machine is underfilling the bags. A 26 bag sample had a mean of 421 grams with a standard deviation of 20. Assume the population is normally distributed. A level of significance of 0.02 will be used. Find the P-value of the test statistic. You may write the P-value as a range using interval notation, or as a decimal value rounded to four decimal places. Answer 2 Points Tables Keypad Keyboard Shortcuts Ne Prev

Answer 1

Solution:

The null and alternative hypothesis are

H₀ : $\mu$ = 427 vs H_a : $\mu$ < 427

The test statistic t is

t =  
T-]/[s/n
= [421 - 427]/[20 /$\sqrt{}$26] = -1.530

Now ,

d.f. = n - 1 = 26 - 1 = 25

< sign in Ha indicates that the test is One tailed right sided .

t = -1.530

So , using calculator ,

p value = 0.0693

Answer is

0.0693

or

(0.05, 0.10)