A publisher reports that 41%41% of their readers own a particular make of car.  A marketing executive wants to test the claim that the percentage is actually different from the reported percentage.  A random sample of 240240 found that 35%35% of the readers owned a particular make of car.  Determine the P-value of the test statistic.  Round your answer to four decimal places.

We are asked to determine the P-value for a hypothesis test concerning proportions.

### Step 1: Define the hypotheses
We want to test whether the proportion of car owners is different from the reported value of 41%. Thus, the null and alternative hypotheses are:

- **Null hypothesis (\(H_0\))**: \( p = 0.41 \) (the true proportion is 41%)
- **Alternative hypothesis (\(H_a\))**: \( p \neq 0.41 \) (the true proportion is different from 41%)

This is a two-tailed test since we are testing whether the proportion is different, not specifically greater or less.

### Step 2: Test statistic formula
We will use a Z-test for proportions. The test statistic \(Z\) is given by:

\[
Z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}}
\]

Where:
- \(\hat{p}\) is the sample proportion,
- \(p_0\) is the population proportion under the null hypothesis (0.41),
- \(n\) is the sample size.

### Step 3: Calculate the values
- \( \hat{p} = 0.35 \) (35% from the sample),
- \( p_0 = 0.41 \),
- \( n = 240 \).

Let's plug these values into the formula and calculate the Z-statistic.

\[
Z = \frac{0.35 - 0.41}{\sqrt{\frac{0.41(1 - 0.41)}{240}}}
\]

Let me calculate the Z-statistic.It seems like I can’t do more advanced data analysis right now. Please try again later. Would you like to try solving this by hand, or upload a photo of the calculations for assistance?

Here are 5 related questions you might find useful:

1. How can we interpret the P-value in hypothesis testing?
2. What is the significance level (\(\alpha\)) used for this hypothesis test?
3. How would the test change if the executive wanted to test whether the proportion is **less** than 41%?
4. Can you explain the difference between one-tailed and two-tailed hypothesis tests?
5. What does the Z-test for proportions assume about the distribution of data?

**Tip:** When performing hypothesis tests for proportions, ensure that the sample size is large enough so the sampling distribution of the sample proportion is approximately normal.

A publisher reports that 41% of their readers own a particular make of car. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 240 found that 35% of the readers owned a particular make of car. Determine the P-value of the test statistic. Round your answer to four decimal places.

Test the hypothesis that a marketing executive's claim about car ownership differs from the publisher's reported 41%. Learn how to calculate the Z-test statistic and P-value for proportions with a sample size of 240 and a sample proportion of 35%. This problem is ideal for college-level statistics students.

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