Need help with this and thak you in advance!Here's the Data:Rod Length25.4225.8925.2124.3224.7024.1524.4923.2924.1325.7124.6523.2024.8025.9523.4725.8024.2425.2325.1625.2224.5924.5324.7024.8124.4023.4525.2824.0324.3425.1326.0825.7423.7124.1825.1126.2925.6125.4724.3624.5924.2424.9425.9424.1326.1225.1624.8323.4724.9625.3426.0025.1925.6124.6624.4824.6425.9724.4024.5524.1324.8325.6024.6326.0023.5624.5624.3825.1224.9025.8325.4424.9824.8125.0924.2524.0025.9025.4624.3025.2223.3224.5825.6024.7125.8523.2225.8224.9824.9524.2324.6924.4424.0525.1225.2124.9824.2125.8925.2324.8924.9125.7625.6124.8424.8324.1625.7024.5624.8424.2525.4524.1525.0025.2326.0025.2224.0624.9424.7925.0425.7424.9125.6624.5726.7323.2225.8524.2924.6825.2925.7124.6324.4325.9625.5224.7124.3625.1124.4525.8724.7224.2324.7425.5925.4524.3925.4624.0725.3925.50 ## Statistical Analysis of Manufacturing Data### ObjectiveA factory manufactures steel rods, which are supposed to have a mean length of 25 cm. If evidence at \(\alpha = 0.05\) shows the mean length is different from 25 cm, the factory will shut down due to potential customer dissatisfaction and maintenance issues. A random sample of 150 rods is taken, with lengths provided in the file **rods20.xls**.### Tasks1. **Make a Frequency Table and Histogram** - Organize the data with the first class of lengths (20, 23.5). 2. **Conduct a Hypothesis Test** - Test if the mean length of the rods is different from 25 cm.3. **Conclusions and Recommendations** - Based on the test results, decide if shutting down the factory is necessary. 4. **Understanding Errors** - Define: - **Type I Error**: Rejecting a true null hypothesis (false positive). - **Type II Error**: Failing to reject a false null hypothesis (false negative). 5. **Error Consequences** - Discuss potential outcomes of making Type I and Type II errors in this context. 6. **Confidence Interval** - Find and interpret a 95% confidence interval for the rod lengths.7. **Final Recommendations** - Decide on shutting down the factory based on the confidence interval. Justify your decision. 8. **Comparative Analysis** - Compare and contrast conclusions from hypothesis testing and confidence intervals.### Notes- **Goal**: Use the data for practical learning.- **Data Management**: Save all files and data diligently.### Lab Report Requirements- Include frequency table, histogram, and hypothesis tests in your report.- Report both the test statistic and p-value, decide on \(H_0\), and summarize your findings.- Use accurate and concise data representation—include tables and graphs for clarity.- Precision: Use thousandths where applicable. Remember, thorough preparation and analysis in this project are critical for practical learning and decision-making in a manufacturing context.

Name: Need help with this and thak you in advance!Here's the Data:Rod Length
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: Need help with this and thak you in advance!Here's the Data:Rod Length25.4225.8925.2124.3224.7024.1524.4923.2924.1325.7124.6523.2024.8025.9523.4725.8024.2425.2325.1625.2224.5924.5324.7024.8124.4023.4525.2824.0324.3425.1326.0825.7423.7124.1825.1126.29

Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a time so we are answering the first three as you have not mentioned which of these you are looking for. Please re-submit the question separately for the remaining sub-parts. As per the given data set, Sample size(n)=150 Level of significance (L)=0.051). As per the given data set, The frequency distribution for the rod lenght dataset would be: Lower-class Upper class (less than) Frequency 23.00 23.50 8 23.50 24.00 2 24.00 24.50 34 24.50 25.00 41 25.00 25.50 30 25.50 26.00 28 26.00 26.50 6 26.50 27.00 12). To test the claim that the mean length for all roads is different from 25 cm or not. Therefore, the null and alternative hypotheses are: H0:μ=25H1:μ=25To test the null hypothesis, the t-test because the population standard deviation is unknown. Formula to compute the t-test statistic value, tstatistic=x¯-μsn Further, the sample mean and standard deviation for the rod length, can be calculated as: Sample meanx¯=∑ixin =25.42+25.89+...+25.39+25.50150 =24.9039 Sample standard deviations=∑ixi-x¯2n-1 =25.42-24.90392+...+25.50-24.90392150-1 =0.7162The t-test statistic value, can be calculated as: tstatistic=24.9039-250.7162150 =-1.6434 Thus, the test statistic value is -1.6434. The p-value at 0.05 level of significance 149 df (df=n-1), can be calculated as: p-value=2PtL2,df>tstatistic =2Pt0.052,149>tstatistic =0.1024 Decision: The null hypothesis is rejected when the p-value is less than the level of significance. Here, the p-value (0.1024) is greater than the level of significance (0.05). Thus, the null hypothesis is not rejected. Therefore, there is no enough evidence to conclude that the mean length for all rods is different from 25cm.3). As per the above part 2), There is no enough evidence to conclude that the mean length for all rods is different from 25cm. Conclusion: The factory will not be shut down and their customer will be happy because the mean length for all rods is not different from 25cm.

Answered: Need help with this and thak you in…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Rod Length
25.42
25.89
25.21
24.32
24.70
24.15
24.49
23.29
24.13
25.71
24.65
23.20
24.80
25.95
23.47
25.80
24.24
25.23
25.16
25.22
24.59
24.53
24.70
24.81
24.40
23.45
25.28
24.03
24.34
25.13
26.08
25.74
23.71
24.18
25.11
26.29
25.61
25.47
24.36