Answer to Question #201510 in Statistics and Probability for grace

Question

It is claimed that the average weight of a bag of biscuits is 250 grams with a standard deviation of 20.5 grams Would you agree to this claim if a random

Answer 1

Would you agree to this claim if random sample of 50 bags of biscuits showed an average weight of 240 grams, using a 0.05 level of significance? 

Null Hypothesis $H_0:\mu=250$

Alternate Hypothesis $H_1:\mu\neq 250$

Standard deviation $\sigma =20.5$

The population standard deviation is known and the sample size $𝑛$ is large $(𝑛 ≥ 30)$

Hence, the test static is $z=\dfrac{\bar x-\mu}{\sigma/\sqrt n}$ and

the value is $z=\dfrac{\bar x-\mu}{\sigma/\sqrt n}=\dfrac{240-255}{20.5/\sqrt{50}}=-5.174$

The test is two tailed (because $𝐻_1$ contains inequality $≠$ ) and the critical values are $𝑧_{−0.025} = −1.96$ and $𝑧_{0.025} = 1.96$ . Since $𝑧 < −𝑧_{0.025}$ , i.e. the $𝑧$ lies to the left of the critical value, we reject the null hypothesis. 

We would not agree with a claim, the true average weight of a bag of biscuits is not 250 grams. Answer: the true average weight of a bag of biscuits is not 250 grams

Answer: The true average weight of a bag of biscuit is not 250 grams.