Test the claim that the proportion of people who own cats is smaller than 40% at the 0.01 significance level. The null and alternative hypothesis would be: Ho:p H1:p + 0.4 H:p> 0.4 H1:µ # 0.4 H1: µ 0.4 Но:р < 0.4 Но:р — 0.4 Но: р < 0.4 Нo:д > 0.4 Но:р > 0.4 0.4 H1:µ < 0.4 H1:p < 0.4 The test is: right-tailed two-tailed left-tailed Based on a sample of 400 people, 32% owned cats The test statistic is: (to 2 decimals) The p-value is: (to 2 decimals) Based on this we: O Fail to reject the null hypothesis Reject the null hypothesis

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### Hypothesis Testing: Proportion of People Who Own Cats

**Problem Statement:** Test the claim that the proportion of people who own cats is smaller than 40% at the 0.01 significance level.

**Step 1: Hypothesis Formulation**
The null and alternative hypotheses would be:

\[
\begin{aligned}
H_0: p &= 0.4 \\
H_1: p &< 0.4 
\end{aligned}
\]

**Step 2: Determining the Type of Test**
The test is:
- Right-tailed \( \circ \)
- Two-tailed \( \circ \)
- Left-tailed \( \bullet \)

**Step 3: Sample Data Information**
Based on a sample of 400 people, 32% owned cats.

**Step 4: Calculate Test Statistic and P-Value**
The test statistic is (to 2 decimals): 
\[ \boxed{\text{\_\_\_\_}} \]

The p-value is (to 2 decimals): 
\[ \boxed{\text{\_\_\_\_}} \]

**Step 5: Decision Making**
Based on this we:
- Fail to reject the null hypothesis \( \circ \)
- Reject the null hypothesis \( \circ \)

Please fill in the blank values (test statistic and p-value) based on the calculations related to the test. This information is key in determining whether to reject the null hypothesis or not.
Transcribed Image Text:### Hypothesis Testing: Proportion of People Who Own Cats **Problem Statement:** Test the claim that the proportion of people who own cats is smaller than 40% at the 0.01 significance level. **Step 1: Hypothesis Formulation** The null and alternative hypotheses would be: \[ \begin{aligned} H_0: p &= 0.4 \\ H_1: p &< 0.4 \end{aligned} \] **Step 2: Determining the Type of Test** The test is: - Right-tailed \( \circ \) - Two-tailed \( \circ \) - Left-tailed \( \bullet \) **Step 3: Sample Data Information** Based on a sample of 400 people, 32% owned cats. **Step 4: Calculate Test Statistic and P-Value** The test statistic is (to 2 decimals): \[ \boxed{\text{\_\_\_\_}} \] The p-value is (to 2 decimals): \[ \boxed{\text{\_\_\_\_}} \] **Step 5: Decision Making** Based on this we: - Fail to reject the null hypothesis \( \circ \) - Reject the null hypothesis \( \circ \) Please fill in the blank values (test statistic and p-value) based on the calculations related to the test. This information is key in determining whether to reject the null hypothesis or not.
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