The display provided from technology available below results from using data for a smartphone carrier's data speeds at airports to test the claim that they are from a population having a mean less than 4.00 Mbps. Conduct the hypothesis test using these results. Use a 0.05 significance level. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim Click the icon to view the display from technology Assuming all conditions for conducting a hypothesis test are met, what are the null and alternative hypotheses? OA Ho <4.00 Mbps OE Ho 4.00 Mbps H₁4.00 Mbps H₁ <4.00 Mbps OC. Ho 4.00 Mbps H₂>4.00 Mbps OD. Ho: -4.00 Mbps H₁4.00 Mbps Identify the test statistic (Round to two decimal places as needed.) Identify the P-value. (Round to three decimal places as needed.) State the final conclusion that addresses the original claim H There is evidence to support the claim that the sample is from a population with a mean less than 4.00 Mbps

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### Hypothesis Testing for Smartphone Carrier's Data Speeds

#### Problem Statement
The display provided from technology available below results from using data for a smartphone carrier's data speeds at airports to test the claim that they are from a population having a mean less than 4.00 Mbps. Conduct the hypothesis test using these results. Use a 0.05 significance level. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.

#### Null and Alternative Hypotheses
Assuming all conditions for conducting a hypothesis test are met, what are the null and alternative hypotheses?

- **Option A:** 
  - Null Hypothesis (H₀): μ ≥ 4.00 Mbps
  - Alternative Hypothesis (H₁): μ < 4.00 Mbps

- **Option B:** 
  - Null Hypothesis (H₀): μ = 4.00 Mbps
  - Alternative Hypothesis (H₁): μ < 4.00 Mbps

- **Option C:** 
  - Null Hypothesis (H₀): μ ≥ 4.00 Mbps
  - Alternative Hypothesis (H₁): μ ≠ 4.00 Mbps

- **Option D:** 
  - Null Hypothesis (H₀): μ = 4.00 Mbps
  - Alternative Hypothesis (H₁): μ ≠ 4.00 Mbps

- **Option E:** 
  - Null Hypothesis (H₀): μ = 4.00 Mbps
  - Alternative Hypothesis (H₁): μ > 4.00 Mbps

#### Identifying Test Statistics
- **Round to two decimal places as needed.**

#### Identifying the P-Value
- **Round to three decimal places as needed.**

#### Final Conclusion
State the final conclusion that addresses the original claim:

H₀: **There is** [__fill in__] **evidence to support the claim that the sample is from a population with a mean less than 4.00 Mbps.**

---

In this problem, you would typically choose the correct null and alternative hypotheses and then perform statistical analysis to find the test statistic and the P-value. Based on the P-value compared to the significance level (0.05), you would draw a conclusion to either reject the null hypothesis or fail to reject it. If rejected, you would have evidence to support the
Transcribed Image Text:### Hypothesis Testing for Smartphone Carrier's Data Speeds #### Problem Statement The display provided from technology available below results from using data for a smartphone carrier's data speeds at airports to test the claim that they are from a population having a mean less than 4.00 Mbps. Conduct the hypothesis test using these results. Use a 0.05 significance level. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim. #### Null and Alternative Hypotheses Assuming all conditions for conducting a hypothesis test are met, what are the null and alternative hypotheses? - **Option A:** - Null Hypothesis (H₀): μ ≥ 4.00 Mbps - Alternative Hypothesis (H₁): μ < 4.00 Mbps - **Option B:** - Null Hypothesis (H₀): μ = 4.00 Mbps - Alternative Hypothesis (H₁): μ < 4.00 Mbps - **Option C:** - Null Hypothesis (H₀): μ ≥ 4.00 Mbps - Alternative Hypothesis (H₁): μ ≠ 4.00 Mbps - **Option D:** - Null Hypothesis (H₀): μ = 4.00 Mbps - Alternative Hypothesis (H₁): μ ≠ 4.00 Mbps - **Option E:** - Null Hypothesis (H₀): μ = 4.00 Mbps - Alternative Hypothesis (H₁): μ > 4.00 Mbps #### Identifying Test Statistics - **Round to two decimal places as needed.** #### Identifying the P-Value - **Round to three decimal places as needed.** #### Final Conclusion State the final conclusion that addresses the original claim: H₀: **There is** [__fill in__] **evidence to support the claim that the sample is from a population with a mean less than 4.00 Mbps.** --- In this problem, you would typically choose the correct null and alternative hypotheses and then perform statistical analysis to find the test statistic and the P-value. Based on the P-value compared to the significance level (0.05), you would draw a conclusion to either reject the null hypothesis or fail to reject it. If rejected, you would have evidence to support the
### T-Test Result Display from Technology

#### Variables
- **Population Mean (µ)**: Less than 4.00
- **Test Statistic (t)**: -3.825604
- **P-value (p)**: 0.000185
- **Sample Mean (x̄)**: 3.38
- **Sample Standard Deviation (Sx)**: 1.145979
- **Sample Size (n)**: 50

#### Explanation of Results

- **Population Mean (µ)**: The hypothesis test evaluates whether the true population mean is less than 4.00.
- **Test Statistic (t)**: The calculated t-value is -3.825604, which indicates how many standard deviations the sample mean is from the hypothesized population mean.
- **P-value (p)**: With a p-value of 0.000185, which is less than the significance level (commonly 0.05), the result is statistically significant, leading us to reject the null hypothesis.
- **Sample Mean (x̄)**: The average value of the sample data is 3.38.
- **Sample Standard Deviation (Sx)**: The variability or dispersion of the sample data points around the sample mean is 1.145979.
- **Sample Size (n)**: The number of observations or data points in the sample is 50.

This data helps in conducting a T-Test to infer if there is enough statistical evidence to say that the population mean is less than 4.0 based on the given sample data.
Transcribed Image Text:### T-Test Result Display from Technology #### Variables - **Population Mean (µ)**: Less than 4.00 - **Test Statistic (t)**: -3.825604 - **P-value (p)**: 0.000185 - **Sample Mean (x̄)**: 3.38 - **Sample Standard Deviation (Sx)**: 1.145979 - **Sample Size (n)**: 50 #### Explanation of Results - **Population Mean (µ)**: The hypothesis test evaluates whether the true population mean is less than 4.00. - **Test Statistic (t)**: The calculated t-value is -3.825604, which indicates how many standard deviations the sample mean is from the hypothesized population mean. - **P-value (p)**: With a p-value of 0.000185, which is less than the significance level (commonly 0.05), the result is statistically significant, leading us to reject the null hypothesis. - **Sample Mean (x̄)**: The average value of the sample data is 3.38. - **Sample Standard Deviation (Sx)**: The variability or dispersion of the sample data points around the sample mean is 1.145979. - **Sample Size (n)**: The number of observations or data points in the sample is 50. This data helps in conducting a T-Test to infer if there is enough statistical evidence to say that the population mean is less than 4.0 based on the given sample data.
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