Answer all the questions ### Hypothesis Testing for Population Mean**Scenario:**You are using technology to test a claim about the population mean, \(\mu\), at a given level of significance, \(\alpha\). The sample statistics are provided, and it's assumed that the population is normally distributed.- **Claim:** \(\mu > 1270\)- **Significance Level (\(\alpha\)):** 0.05- **Standard Deviation (\(\sigma\)):** 208.23- **Sample Statistics:** - Sample Mean (\(\bar{x}\)): 1295.06 - Sample Size (\(n\)): 300**Task:**Identify the null and alternative hypotheses.**Options:**- **A.** - \(H_0: \mu \geq 1295.06\) - \(H_a: \mu < 1295.06\)- **B.** - \(H_0: \mu \geq 1270\) - \(H_a: \mu < 1270\)- **C.** - \(H_0: \mu \leq 1270\) - \(H_a: \mu > 1270\)- **D.** - \(H_0: \mu \leq 1270\) - \(H_a: \mu > 1270\)- **E.** - \(H_0: \mu \leq 1295.06\) - \(H_a: \mu > 1295.06\)- **F.** - \(H_0: \mu \geq 1295.06\) - \(H_a: \mu < 1295.06\)**Calculation:****Calculate the standardized test statistic:**Enter the test statistic in the provided box, and round to two decimal places.**P-Value:**Determine the P-value using the software tools.**Navigation Button:**- Next (to proceed to the next step in the testing process)This section prepares students to set up hypothesis tests and understand the process of calculating and interpreting statistics related to claims about population means. ### Hypothesis Testing ExampleThis screenshot provides an example of how to conduct a hypothesis test to evaluate a claim about a population mean \( \mu \) at a given significance level \( \alpha \).#### Given Information:- Claim: \( \mu > 1270 \)- Significance Level: \( \alpha = 0.05 \)- Population Standard Deviation: \( \sigma = 208.23 \)- Sample Size: \( n = 300 \)- Sample Mean: \( \bar{x} = 1295.06 \)#### Hypotheses:Two sets of hypotheses are provided for selection:1. **Option E:** - Null Hypothesis (\( H_0 \)): \( \mu \leq 1295.06 \) - Alternative Hypothesis (\( H_a \)): \( \mu > 1295.06 \)2. Additional options (not clearly visible) appear to involve similar hypothesis structures either testing \( \mu \neq 1270 \) or other values around 1295.06.#### Calculations:- **Calculate the Standardized Test Statistic:** A space is provided for the standardized test statistic, typically calculated as: \[ z = \frac{\bar{x} - \mu_0}{\sigma/\sqrt{n}} \] Where \( \mu_0 \) is the mean specified under the null hypothesis.- **Determine the P-value:** A place is provided to round the P-value to three decimal places, which is used for the decision-making process.#### Decision:- Based on the calculated P-value, you will either "Fail to reject" or "Reject" the null hypothesis.The conclusion is meant to state:- "At the 5% significance level, there is **not** enough evidence to reject the claim." #### Instructions:- Calculate the test statistic.- Determine the P-value.- Decide whether to reject or fail to reject the null hypothesis based on the P-value and significance level.

Given,sample size(n)=300sample mean(x¯)=1295.06Standard deviation(σ)=208.23claim: μ>1270α=0.05

Use technology to help you test the claim about the population mean, u, at the giveh level 8l sighilica population is normally distributed. Claim: u> 1270; a=0.05; o=208.23. Sample statistics: x= 1295.06, n= 300 Identify the null and alternative hypotheses. Choose the correct answer below. O A. Ho: µ> 1295.06 O B. Ho: µ> 1270 H us 1270 Ha us 1295.06 O C. Ho: us 1270 Ο D . H μ2 1270 Ha µ< 1270 Ha: µ> 1270 t O E. Ho:µS 1295.06 Ha: u> 1295.06 OF. Ho: H2 1295.06 Ha µ< 1295.06 Ma Calculate the standardized test statistic.. det The standardized test statistic is Mis (Round to two decimal places as needed.) Determine the P-value http (L1) More Sta Ste Next Wh sim

Use technology to help you test the claim about the population mean, u, at the giveh level 8l sighilica population is normally distributed. Claim: u> 1270; a=0.05; o=208.23. Sample statistics: x= 1295.06, n= 300 Identify the null and alternative hypotheses. Choose the correct answer below. O A. Ho: µ> 1295.06 O B. Ho: µ> 1270 H us 1270 Ha us 1295.06 O C. Ho: us 1270 Ο D . H μ2 1270 Ha µ< 1270 Ha: µ> 1270 t O E. Ho:µS 1295.06 Ha: u> 1295.06 OF. Ho: H2 1295.06 Ha µ< 1295.06 Ma Calculate the standardized test statistic.. det The standardized test statistic is Mis (Round to two decimal places as needed.) Determine the P-value http (L1) More Sta Ste Next Wh sim

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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