Question

Write the null and alternative hypothesis of given problem:

    1. It is claimed that the average weight of a bag of biscuit is 250 grams with a standard deviation of 20.5 grams. Would you agree to this claim if a random sample of 50 bags of biscuits showed an average weight of 240 grams, using a 5% level of significance.

Answer 1

Solution:

Null hypothesis, $H_0:\mu=250$

Alternative hypothesis, $H_1:\mu\ne250$

Assume that the population standard deviation is $\sigma=20.5$ . The population standard deviation is known and the sample size n is large $(n \geq 30)$ . Hence, the test statistic is $z=\frac{\bar{x}-\mu}{\sigma / \sqrt{n}}$ , and the value is $z=\frac{\bar{x}-\mu}{\sigma / \sqrt{n}}=\frac{240-255}{20.5 / \sqrt{50}}=-5.174$ . The test is two tailed (because H₁ contains inequality $\neq$ ) 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.