Business Context
WidgetCorp, a manufacturer of precision widgets, aims to ensure its production process maintains a consistent average weight of 50 grams. Quality assurance conducts periodic sampling of widgets to monitor this average weight.
Problem Statement
Given the population standard deviation of widget weights is known to be 5 grams, determine if the sample mean from a recent batch of 30 widgets significantly deviates from the target mean of 50 grams.
Given Data
| Parameter | Value |
|---|
| Population Mean (μ) | 50 grams |
| Population Std Dev (σ) | 5 grams |
| Sample Size (n) | 30 |
| Sample Mean (x̄) | 52 grams |
| Significance Level (α) | 0.05 |
Requirements
- State the null and alternative hypotheses.
- Calculate the standard error of the mean (SEM).
- Compute the z-test statistic for the sample mean.
- Determine the p-value for the z-test statistic.
- Make a decision regarding the null hypothesis based on the p-value.
- Interpret the results in the context of WidgetCorp's production quality control.
Assumptions
- The sample is randomly selected from the population of widget weights.
- The distribution of widget weights is approximately normal, or the sample size is sufficiently large to invoke the Central Limit Theorem.
