Questions: Cost of Rolex Watches The average cost of a Rolex watch is 7521. A researcher selected a random sample of 40 jewelry stores and found the average cost of Rolex watches was 7350. If sigma= 99 and alpha=0.05, can it be concluded that the average cost of a Rolex watch in that area is less than 7521 ? Part 1 of 5 (a) State the hypotheses and identify the claim with the correct hypothesis. H0: (Choose one) H1: (Choose one) This hypothesis test is a (Choose one) test. mu > < = ≠ × ddots

Cost of Rolex Watches The average cost of a Rolex watch is 7521. A researcher selected a random sample of 40 jewelry stores and found the average cost of Rolex watches was 7350. If sigma= 99 and alpha=0.05, can it be concluded that the average cost of a Rolex watch in that area is less than 7521 ?

Part 1 of 5
(a) State the hypotheses and identify the claim with the correct hypothesis.

H0: (Choose one)
H1: (Choose one)

This hypothesis test is a (Choose one) test.

mu > <
= ≠
× ddots

Transcript text: Cost of Rolex Watches The average cost of a Rolex watch is $\$ 7521$. A researcher selected a random sample of 40 jewelry stores and found the average cost of Rolex watches was $\$ 7350$. If $\sigma=\$ 99$ and $\alpha=0.05$, can it be concluded that the average cost of a Rolex watch in that area is less than $\$ 7521$ ? Part 1 of 5 (a) State the hypotheses and identify the claim with the correct hypothesis. \[ \begin{array}{l} H_{0}: \square \text { (Choose one) } \\ H_{1}: \square \text { (Choose one) } \end{array} \] This hypothesis test is a $\square$ (Choose one) test. \begin{tabular}{|ccc|} \hline$\mu$ & $\square>\square$ & $\square<\square$ \\ $\square=\square$ & $\square \neq \square$ & \\ $\times$ & $\ddots$ \\ \hline \end{tabular}

Solution

Solution Steps

Step 1: State the Hypotheses

The hypotheses for this test are defined as follows:

Null Hypothesis: $ H_0: \mu = 7521 $
Alternative Hypothesis: $ H_1: \mu < 7521 $

This hypothesis test is a left-tailed test.

Step 2: Calculate the Z-Score

The Z-score is calculated using the formula: \[ z = \frac{X - \mu}{\sigma / \sqrt{n}} \] Substituting the values: \[ z = \frac{7350 - 7521}{99 / \sqrt{40}} \approx -10.9242 \]

Step 3: Calculate the P-Value

The P-value associated with the calculated Z-score is: \[ \text{P-value} \approx 4.4158 \times 10^{-28} \]

Step 4: Determine the Critical Value

For a left-tailed test at a significance level of $ \alpha = 0.05 $, the critical value is: \[ Z_{\text{critical}} \approx -1.96 \]

Step 5: Make a Decision

Since the calculated Z-score $ z \approx -10.9242 $ is less than the critical value $ -1.96 $, we reject the null hypothesis.