Question #181439

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?


1
Expert's answer
2021-04-15T06:51:25-0400

μ=440σ=20n=100xˉ=435α=0.05H0:μ=440H1:μ440\mu = 440 \\ \sigma = 20 \\ n = 100 \\ \bar{x} = 435 \\ α = 0.05 \\ H_0 : \mu = 440 \\ H_1 : \mu ≠ 440

Test concerning averages

z=xˉμσ/nz=43544020/100=2.5z = \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.


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