Question

Question 10 - of 16 Step 4 of 5 00:54:33 A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 445 gram setting. Based on a 12 bag sample where the mean is 441 grams and the variance is 441, is there sufficient evidence at the 0.025 level that the bags are underfilled? Assume the population distribution is approximately normal. Step 4 of 5: Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places. Answer How to Enter) 3 Points Keypad Reject Hoift < U 3 ng.com/Portal Test/Testlake Test re to search o

Answer 1

Solution :

This is the left tailed test,  

The null and alternative hypothesis is ,

H₀ :  $\mu$ = 445

H_a : $\mu$ < 445

s = $\sqrt{}$ s² = $\sqrt{}$ 441 = 21

Test statistic = t =

= (
T
- $\mu$ ) / s / $\sqrt$ n

= (441 - 445) / 21 / $\sqrt$ 12

Test statistic = t = -0.660

$\alpha$ = 0.025

degrees of freedom = n - 1 = 12 - 1 = 11

P(t < t ) = 0.025

= P(t < -2.201 ) = 0.025

t = -2.201

Reject H_O , test statistic > critical value

Reject H_O if t < -2.201