A wedding website states that the average cost of a wedding is $26,706
. One concerned bride hopes that the average is less than reported. To see if her hope is correct, she surveys 35
recently married couples and finds that the average cost of weddings in the sample was $24,365
. Assuming that the population standard deviation is $6575
, is there sufficient evidence to support the bride’s hope at the 0.05
level of significance?
Step 2 of 3 :  Compute the value of the test statistic. Round your answer to two decimal places.

To compute the value of the test statistic for this hypothesis test, we will use the following steps:

### Step 1: Set Up the Hypotheses

- **Null Hypothesis (H₀):** $\mu \geq 26,706$ (The average cost of weddings is at least $26,706)
- **Alternative Hypothesis (H₁):** $\mu < 26,706$ (The average cost of weddings is less than $26,706)

### Step 2: Identify the Test Statistic Formula

Since the population standard deviation ($\sigma$) is known, we will use the **z-test** statistic formula:

\[
z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}
\]

Where:
- $\bar{x} = 24,365$ (Sample mean)
- $\mu = 26,706$ (Population mean)
- $\sigma = 6,575$ (Population standard deviation)
- $n = 35$ (Sample size)

### Step 3: Compute the Test Statistic

Plug in the values into the z-test formula:

\[
z = \frac{24,365 - 26,706}{\frac{6,575}{\sqrt{35}}}
\]

First, calculate the denominator (standard error):

\[
\text{Standard Error} = \frac{6,575}{\sqrt{35}} \approx \frac{6,575}{5.9161} \approx 1,111.14
\]

Now, compute the z-value:

\[
z = \frac{24,365 - 26,706}{1,111.14} \approx \frac{-2,341}{1,111.14} \approx -2.11
\]

### Final Answer

The value of the test statistic is approximately **-2.11**.

Would you like more details or have any other questions?

Here are five related questions you might find helpful:
1. How do you interpret the value of the test statistic in this context?
2. What would be the next step to conclude this hypothesis test?
3. How is the level of significance used in this hypothesis test?
4. How would the test statistic change if the sample size were larger?
5. Can the bride's hope be confirmed if the test statistic is less than the critical value?

**Tip:** Always compare the test statistic to the critical value (from the z-table) to make a decision in hypothesis testing.

Explore hypothesis testing in statistics with a real-world example of wedding costs. Analyze if there is sufficient evidence to support a bride's hope that wedding costs are lower than reported. Calculate the z-test statistic with detailed steps and formulas.

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