Answer to Question #181439 in Statistics and Probability for Kapolyo

Question

A manufacturer claims that the average weight of a tin of baked beans in 440g and the standard deviation is known to be 20g. From a random sample of 100 cans you calculate the average weight to be 435g. At the 95% level of confidence, is there a change in the average weight of a can of baked beans?

Answer 1

$\mu = 440 \\ \sigma = 20 \\ n = 100 \\ \bar{x} = 435 \\ α = 0.05 \\ H_0 : \mu = 440 \\ H_1 : \mu ≠ 440$

Test concerning averages

$z = \frac{\bar{x}- \mu}{\sigma / \sqrt{n}} \\ z = \frac{435-440}{20/ \sqrt{100}} = -2.5$

Critical value at 0.05 significance level with 99 d.f. z = ±1.96

Critical regions: Two-tailed test. Reject H₀ if z ≤ -1.96 or z≥1.96

Conclusion: Since z = -2.5 is less than -1.96, reject the null hypothesis at the 95% level of confidence. There is a change in the average weight of a can of baked beans.