Certainly! If we opt to perform a **Z-test** instead of a \( t \)-test, we'll assume that either the sample size is large enough (which it is, with \( n = 35 \)), or we know the population standard deviation (which we do, given the previous month's standard deviation of 1.2 minutes).

### Hypothesis Setup

- **Null Hypothesis (\( H_0 \))**: The mean waiting time during the sales season is equal to the previous month's average waiting time.
  \[
  H_0: \mu = 4.5 \text{ minutes}
  \]

- **Alternative Hypothesis (\( H_1 \))**: The mean waiting time during the sales season is different from the previous month's average waiting time.
  \[
  H_1: \mu \neq 4.5 \text{ minutes}
  \]

### Significance Level

The significance level (\( \alpha \)) is 0.05.

### Test Statistic

The test statistic for a Z-test is calculated as follows:
\[
Z = \frac{\bar{x} - \mu_0}{\frac{\sigma}{\sqrt{n}}}
\]
Where:
- \( \bar{x} \) is the sample mean
- \( \mu_0 \) is the hypothesized population mean (4.5 minutes)
- \( \sigma \) is the population standard deviation (1.2 minutes)
- \( n \) is the sample size (35)

### Decision Rule

For a two-tailed test at the \( \alpha = 0.05 \) significance level, the critical Z-values are \( \pm 1.96 \). If the calculated Z-value falls outside this range, we reject the null hypothesis.

### Steps to Solve

1. **Calculate the sample mean (\( \bar{x} \))** from the provided data.
2. **Compute the Z-statistic** using the formula above.
3. **Compare the Z-statistic** to the critical Z-value of \( \pm 1.96 \).
4. **Make a decision** based on whether the Z-statistic falls within or outside the critical region.

Please provide the sample data so we can calculate the sample mean (\( \bar{x} \)) and proceed with the Z-test.

Learn how to perform a Z-test in hypothesis testing with a step-by-step example. Calculate the Z-test statistic, compare it to critical values, and make decisions based on statistical significance. Suitable for advanced undergraduate students and researchers.

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