ribution as an approximation to the binomial distribution, and assume a 0.05 significance level to complete parts (a) through (e). st of p=0.9 vs p*0.9 ample X N 2,082 1836 Sample p 0.881844 95% CI Z-Value P-Value 0.006 (0.867979,0.895710) -2.76 a. Is the test two-tailed, left-tailed, or right-tailed? O Left-tailed test O Two-tailed test O Right tailed test b. What is the test statistic? The test statistic is D

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I need the test statistic also along with the p value, null hypothesis
**Title: Statistical Analysis of Cell Phone Ownership**

**Introduction:**
A survey was conducted on 2,082 randomly selected adults to investigate cell phone ownership. The study found that 88% of them own cell phones. The following analysis tests the claim that 90% of adults own cell phones, using a significance level of 0.05.

**Statistical Test:**
- **Hypothesis:** Test of \( p = 0.9 \) vs \( p \neq 0.9 \)
- **Sample Details:**
  - **Sample X (Number of Successes):** 1,836
  - **Sample N (Total Sample Size):** 2,082
  - **Sample p (Sample Proportion):** 0.881844

- **Confidence Interval (CI):** 95% CI for the population proportion is (0.867979, 0.895710).

- **Z-Value:** -2.76
- **P-Value:** 0.006

**Questions:**
a. **Is the test two-tailed, left-tailed, or right-tailed?**
   - Options:
     - Left-tailed test
     - Two-tailed test
     - Right-tailed test

b. **What is the test statistic?**

**Analysis Description:**
The analysis utilizes a normal distribution approximation to the binomial distribution. A Z-test was applied to compare the sample proportion with the claimed proportion. The p-value indicates the probability of observing the given results if the null hypothesis were true.

**Conclusion:**
Based on the provided p-value of 0.006, the null hypothesis can be rejected at the 0.05 significance level, suggesting that the proportion of adults who own cell phones is significantly different from 90%. The test employed was likely two-tailed, given the set hypothesis setup.
Transcribed Image Text:**Title: Statistical Analysis of Cell Phone Ownership** **Introduction:** A survey was conducted on 2,082 randomly selected adults to investigate cell phone ownership. The study found that 88% of them own cell phones. The following analysis tests the claim that 90% of adults own cell phones, using a significance level of 0.05. **Statistical Test:** - **Hypothesis:** Test of \( p = 0.9 \) vs \( p \neq 0.9 \) - **Sample Details:** - **Sample X (Number of Successes):** 1,836 - **Sample N (Total Sample Size):** 2,082 - **Sample p (Sample Proportion):** 0.881844 - **Confidence Interval (CI):** 95% CI for the population proportion is (0.867979, 0.895710). - **Z-Value:** -2.76 - **P-Value:** 0.006 **Questions:** a. **Is the test two-tailed, left-tailed, or right-tailed?** - Options: - Left-tailed test - Two-tailed test - Right-tailed test b. **What is the test statistic?** **Analysis Description:** The analysis utilizes a normal distribution approximation to the binomial distribution. A Z-test was applied to compare the sample proportion with the claimed proportion. The p-value indicates the probability of observing the given results if the null hypothesis were true. **Conclusion:** Based on the provided p-value of 0.006, the null hypothesis can be rejected at the 0.05 significance level, suggesting that the proportion of adults who own cell phones is significantly different from 90%. The test employed was likely two-tailed, given the set hypothesis setup.
**Question: Statistical Hypothesis Testing**

Choose the correct answer below:

**A.** Fail to reject the null hypothesis because the P-value is greater than the significance level, α.

**B.** Reject the null hypothesis because the P-value is greater than the significance level, α.

**C.** Fail to reject the null hypothesis because the P-value is less than or equal to the significance level, α.

**D.** Reject the null hypothesis because the P-value is less than or equal to the significance level, α.

**e.** What is the final conclusion?

---

The screen displays a multiple-choice question related to statistical hypothesis testing with four options. The question focuses on how to interpret the P-value in relation to a given significance level, α. There are no graphs or diagrams present, just text for a quiz or educational exercise.
Transcribed Image Text:**Question: Statistical Hypothesis Testing** Choose the correct answer below: **A.** Fail to reject the null hypothesis because the P-value is greater than the significance level, α. **B.** Reject the null hypothesis because the P-value is greater than the significance level, α. **C.** Fail to reject the null hypothesis because the P-value is less than or equal to the significance level, α. **D.** Reject the null hypothesis because the P-value is less than or equal to the significance level, α. **e.** What is the final conclusion? --- The screen displays a multiple-choice question related to statistical hypothesis testing with four options. The question focuses on how to interpret the P-value in relation to a given significance level, α. There are no graphs or diagrams present, just text for a quiz or educational exercise.
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