Question

6 points 1. Does an average pack of banana bread cookies weighs 40 grams? A random sample of 35 boxes showed a mean of 41.75 grams. The company has specified the population standard deviation to be 5 grams. Test at the 0.05 level of significance. *

Answer 1

Null Hypothesis states that the average pack of banana bread cookies weighs:

$H_{o}:\mu = 40\: grams$

Alternate Hypothesis states the opposite of null Hypothesis:

H: 40 grams

Sample size n = 35

Sample mean $\bar{x} = 41.75\: grams$

$Population\: sd\: \sigma = 5$

Significance level $\alpha$ = 0.05

Since population standard deviation is known we will do z-test:

Test statistics:

n

$= \frac{41.75-40}{\frac{5}{\sqrt{35}}}$

$=2.07$

Test statistics z = 2.07

Test the claim:

Based on Rejection Region: critical value at 0.05 significance for two tailed test is

Since z > z_c (Reject the null Hypothesis)

Based on P-value: P-value is 0.0385 which is less than 0.05

Since p-value < $\alpha$ (we reject the null Hypothesis)

Conclusion: There is enough evidence to support the claim that average weight of banana bread cookies is different from 40 grams.