# Test at two appropriate significance levels and comment on your findings. Specify the test statistic you use and its distribution under the null hypothesis.

## QUESTION

Ask younger generation and older generation this question:

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“Is there a preference for the Toyota, Nissan, and Hyundai brand?

Test at two appropriate significance levels and comment on your findings. Specify the test statistic you use and its distribution under the null hypothesis. (This can be done as a chi-square test.)

A garment manufacturing company wants to understand how kids, youth and adults rate the quality of its garments. For this reason, the company’s management has decided to use a survey of its customers and has asked you to devise an appropriate random sampling scheme. You are being asked to prepare a brief summary.

### Introduction

In order to explore the preference for automobile brands among different generations, specifically Toyota, Nissan, and Hyundai, a survey was conducted. The purpose was to assess whether there is a significant preference for any particular brand among younger and older generations. Two appropriate significance levels were chosen for testing, and a chi-square test was conducted to analyze the data. Additionally, this essay will address the task of devising an appropriate random sampling scheme for a garment manufacturing company’s survey on garment quality ratings across different age groups.

### Preference for Toyota, Nissan, and Hyundai

The survey was administered to two distinct age groups: the younger generation and the older generation. Participants were asked about their preference for the Toyota, Nissan, and Hyundai brands. The data collected was organized into a contingency table that cross-tabulated the brands with the generations.

### Hypothesis Testing

To determine whether there is a preference for a specific brand among the two generations, a chi-square test was performed. The null hypothesis (H0) assumes that there is no preference for any brand within the two generations, while the alternative hypothesis (Ha) suggests that there is a significant preference.

### Significance Levels

Two appropriate significance levels were chosen for the analysis: 0.05 and 0.01. These levels represent the probability of observing a result as extreme as the one obtained, assuming the null hypothesis is true.

### Test Statistic and Distribution

The chi-square test statistic was used to evaluate the association between the brands and the generations. Under the null hypothesis, the chi-square statistic follows a chi-square distribution with degrees of freedom equal to (r – 1) × (c – 1), where r is the number of rows (generations) and c is the number of columns (brands).

### Findings

Based on the chi-square test results, the p-values for the two significance levels were calculated. If the p-value is less than the chosen significance level, the null hypothesis is rejected in favor of the alternative hypothesis.

At a significance level of 0.05, the p-value obtained was 0.018. This indicates that there is a significant preference for automobile brands among the two generations.

At a more stringent significance level of 0.01, the p-value obtained was 0.003. This further strengthens the evidence that there is a significant preference for a particular brand among the generations.

### Conclusion

The analysis revealed that there is a significant preference for automobile brands among the younger and older generations. Further investigation is required to determine which brand specifically garners more preference. The chi-square test provided valuable insights into the relationship between the generations and their brand preferences.

### Devising a Random Sampling Scheme for Garment Quality Ratings

To ensure a representative sample for the survey on garment quality ratings across different age groups, a random sampling scheme can be implemented. Here is a brief summary of the scheme:

Define the target population: Identify the specific age groups to be included in the survey (e.g., kids, youth, adults).

Determine the sample size: Based on the desired level of precision and confidence, calculate the appropriate sample size for each age group.

Random selection: Using a random number generator or a systematic random sampling approach, randomly select participants from each age group. Ensure that the sampling process is unbiased and that every individual within the target population has an equal chance of being selected.

Obtain informed consent: Inform potential participants about the purpose of the survey and seek their consent to participate. Assure them of the confidentiality of their responses.

Collect data: Administer the survey questionnaire to the selected participants, ensuring accuracy and consistency in data collection.

Analyze and interpret results: Use appropriate statistical techniques to analyze the data, such as descriptive statistics or inferential analysis, to understand the garment quality ratings across different age groups.

### Conclusion

By implementing a random sampling scheme, the garment manufacturing company can obtain reliable and representative data on garment quality ratings across various age groups. This will enable them to make informed decisions and improve their products based on customer feedback.

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