Contents

- Researchers were investigating whether there is a significant difference between the number of people who donate to charity when contacted by phone versus those who are not contacted.
- The director of a marketing department wants to estimate the mean number of products purchased per customer last year.
- A survey was conducted in a large city to investigate the relationship between income and satisfaction with the city.
- From a random sample of 1005 people, the mean number of hours spent watching television per week was found to be 20.1.
- Assuming all conditions for inference were met, what can we conclude about the population mean?
- How can we be sure that the conditions for inference were met?
- What are the implications of not meeting the conditions for inference?
- What are some other factors that could affect the results of the study?

A national charity contacted 100 randomly selected people in the United States to ask them how they felt about their experiences with the organization. They received a wide range of responses, and some were quite surprising.

A national charity contacted 100 randomly. The charity wanted to investigate the impact of their work on the community.

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National charity, 100 random people contacted. Researchers investigating whether there is a significant difference. Director of marketing department wants to estimate. Survey was conducted in a large city to investigate. From a random sample of 1005, assuming all conditions for inference were met…

## Researchers were investigating whether there is a significant difference between the number of people who donate to charity when contacted by phone versus those who are not contacted.

The director of a marketing department wants to estimate the percentage of people in the city who would be willing to purchase a new product.:

A survey was conducted in a large city to investigate the relationship between income and number of hours spent watching television. The following table shows the results.

## The director of a marketing department wants to estimate the mean number of products purchased per customer last year.

In order to make accurate estimations, researchers were investigating whether there is a significant difference between the mean number of products purchased per customer last year and the population mean. A survey was conducted in a large city to investigate this matter.

From a random sample of 1005 customers, it was found that the mean number of products purchased per customer last year was 12.5 with a standard deviation of 5.2. Assuming all conditions for inference were met, we can say that there is a 95% chance that the true population mean lies within 2 standard deviations of the sample mean, which means that the population mean is most likely between 2.1 and 23.9.

Therefore, we can estimate that the average customer purchased 12-13 products from the company last year.

## A survey was conducted in a large city to investigate the relationship between income and satisfaction with the city.

The director of a marketing department wants to estimate the mean amount of money spent per person at her store. She takes a random sample of 1005 customers and finds that they spend an average of $54 with a standard deviation of $12. Assuming all conditions for inference were met, what is the 99% confidence interval for the population mean?

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Researchers were investigating whether there is a significant difference in the number of hours that full-time and part-time employees work. A random sample of 36 full-time workers is selected and it is found that they work an average of 42 hours per week with a standard deviation of 5 hours. Another random sample of 64 part-time workers is selected and it is found that they work an average of 28 hours per week with a standard deviationof 4 hours. What is the 95% confidence interval for the difference in means?

## From a random sample of 1005 people, the mean number of hours spent watching television per week was found to be 20.1.

The director of a marketing department wants to estimate the mean number of hours spent watching television per week for all people in the city. He uses a random sample of 1005 people and finds that the mean number of hours spent watching television per week is 20.1.

Assuming all conditions for inference are met, we can use this information to make inferences about the population mean. We can be reasonably confident that the population mean falls somewhere within our confidence interval.

## Assuming all conditions for inference were met, what can we conclude about the population mean?

There is a significant difference between the population mean and the sample mean. This means that the director of a marketing department can estimate that the population of people who live in cities are more likely to shop online than those who live in rural areas.

## How can we be sure that the conditions for inference were met?

In order for us to make inferences from our data, we need to be sure that the conditions for inference have been met. There are four main conditions that need to be met in order for us to make valid inferences:

1) The data must be a random sample

2) The population size must be large enough

3) The sampling method must be appropriate

4) All conditions for inference must be met

Assuming all conditions for inference were met, researchers were investigating whether there is a significant difference in the average amount of time spent on social media between high school students and college students. They collected data from a random sample of 1005 high school students and college students and found that the average amount of time spent on social media by high school students was 2.5 hours per day, while the average amount of time spent on social media by college students was 3.0 hours per day. Based on their results, they concluded that there is a significant difference in the average amount of time spent on social media between high school students and college students.

## What are the implications of not meeting the conditions for inference?

If the conditions for inference are not met, then the conclusions drawn from the data may be inaccurate. This could lead to incorrect decisions being made based on the false information.

## What are some other factors that could affect the results of the study?

There are many factors that could potentially affect the results of a study like this. For example, the specific research methods used (e.g., the type of survey questions asked), the sample size, and the population being studied could all play a role in influencing the results. Additionally, external factors such as current events or public opinion could also impact the findings.

The “random samples of 100 parts from production line a has 12 parts” is a scenario that was recently found out. A National Charity contacted 100 randomly to find out how many parts were missing on their production line.