Cost of Braces The average cost for teeth straightening with metal braces is approximately $$ \$ 5496 $$. A nationwide franchise thinks that its cost is below that figure. A random sample of 28 patients across the country had an average cost of $$ \$ 5157 $$ with a standard deviation of $$ \$ 628 $$. At $$ \alpha=0.005 $$, can it be concluded that the mean is less than $$ \$ 5496 $$ ? Assume that the population is approximately normally distributed. Part: $$ 0 / 5 $$ Part 1 of 5 (a) State the hypotheses and identify the claim. $$ \begin{array}{l} H_{0}=\mu(\text { Choose one }) ~ \$ \square(\text { Choose one) T } \ H_{1}=\mu(\text { Choose one } T \$ \text { (Choose one) } T \end{array} $$ This hypothesis test is a $$ \square $$ (Choose one) test.

Question

UpStudy AI · Accepted Answer

To solve this problem, we need to set up the null and alternative hypotheses based on the information provided.

### Step 1: State the Hypotheses

1. **Null Hypothesis ($$H_0$$)**: This hypothesis states that the mean cost of braces is equal to the average cost of $$ \$ 5496 $$. 
   $$
   H_0: \mu = 5496
   $$

2. **Alternative Hypothesis ($$H_1$$)**: This hypothesis states that the mean cost of braces is less than $$ \$ 5496 $$. 
   $$
   H_1: \mu < 5496
   $$

### Step 2: Identify the Claim

The claim is that the mean cost is less than $$ \$ 5496 $$, which corresponds to the alternative hypothesis.

### Step 3: Type of Test

Since we are testing whether the mean is less than a specific value, this is a **one-tailed test**.

### Summary

Putting it all together, we have:

$$
\begin{array}{l}
H_{0}:\mu = 5496 \
H_{1}:\mu < 5496
\end{array}
$$

This hypothesis test is a **one-tailed** test.
$$ H_0: \mu = 5496 $$ $$ H_1: \mu < 5496 $$ This is a **one-tailed** test.

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Statistics Questions