Explain the key components of hypothesis testing and outline the steps involved in conducting a hypothesis test.

Level of significance ($\alpha$)**: The probability of rejecting the null hypothesis when it is actually true (Type I error). It represents the maximum acceptable risk of making a Type I error.

The procedure for performing a test of a statistical hypothesis is as follows:

1. State the Hypotheses: Formulate the null hypothesis ($H_0$) and the alternative hypothesis ($H_1$).
2. Choose the Test Statistic: Select the appropriate statistical test based on the data type, sample size, and population parameters.
3. Determine the Level of Significance: Set the significance level ($\alpha$), which is the probability of rejecting a true null hypothesis.
4. Calculate the Test Statistic: Compute the value of the test statistic using the sample data.
5. Determine the Critical Region or p-value: Find the critical value(s) from the appropriate distribution table or calculate the p-value.
6. Make a Decision: Compare the calculated test statistic to the critical value(s) or compare the p-value to the level of significance.
7. State the Conclusion: Interpret the decision in the context of the original problem.

We will follow the procedure outlined in (ii) to determine if the proprietor's complaint is justified.

Given Data:

• Population mean (stated value), $\mu_0 = 100$ g
• Sample size, $n = 100$
• Sample mean, $\bar{x} = 99.88$ g
• Sample standard deviation, $s = 0.7$ g
• Level of significance, $\alpha = 0.05$