A Company Claims That Its Tablet Computers Have An Average Recharge Time Of 3 Hours With A Standard Deviation Of 1.4 Hours. Using A Random Sample Of 50 Company Tablet Computers, A Consumer Group Determines A Mean Recharge Time Of 2.5

Mar 13, 2025 by ADMIN 234 views

**A Company's Claim: Is it Reliable?**

Introduction

In today's fast-paced world, technology plays a vital role in our daily lives. With the increasing demand for portable and efficient devices, tablet computers have become a popular choice for both personal and professional use. However, with the rise of technology, comes the need for reliable and accurate information. In this article, we will delve into a company's claim about its tablet computers, specifically their recharge time, and determine if it is reliable.

The Claim

A company claims that its tablet computers have an average recharge time of 3 hours with a standard deviation of 1.4 hours. This claim is based on the company's internal testing and data analysis. However, a consumer group has taken it upon themselves to verify this claim by conducting a random sample of 50 company tablet computers.

The Sample

The consumer group has collected data on the recharge time of 50 company tablet computers. The mean recharge time of these devices is 2.5 hours, with a standard deviation of 1.2 hours. This data is crucial in determining the reliability of the company's claim.

Hypothesis Testing

To determine if the company's claim is reliable, we need to perform a hypothesis test. The null hypothesis (H0) is that the mean recharge time of the company's tablet computers is 3 hours, while the alternative hypothesis (H1) is that the mean recharge time is not equal to 3 hours.

Calculating the Test Statistic

To calculate the test statistic, we need to use the following formula:

t = (x̄ - μ) / (s / √n)

where x̄ is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.

Plugging in the values, we get:

t = (2.5 - 3) / (1.2 / √50) t = -0.5 / 0.15 t = -3.33

Determining the P-Value

The p-value is the probability of observing a test statistic at least as extreme as the one we obtained, assuming that the null hypothesis is true. In this case, we are interested in the two-tailed p-value, which is the probability of observing a test statistic at least as extreme as -3.33 or 3.33.

Using a t-distribution table or calculator, we find that the two-tailed p-value is approximately 0.001.

Interpreting the Results

The p-value of 0.001 is very small, indicating that the observed difference between the sample mean and the population mean is statistically significant. This means that we can reject the null hypothesis and conclude that the mean recharge time of the company's tablet computers is not equal to 3 hours.

Conclusion

In conclusion, the company's claim about its tablet computers having an average recharge time of 3 hours is not reliable. The consumer group's data analysis has shown that the mean recharge time is actually 2.5 hours, with a standard deviation of 1.2 hours. This difference is statistically significant, and we can conclude that the company's claim is not accurate.

Implications

The implications of this study are significant. Consumers who are considering purchasing the company's tablet computers should be aware of the actual recharge time, which is 2.5 hours. This information can help consumers make informed decisions about their purchases.

Future Research

Future research could involve collecting more data on the recharge time of the company's tablet computers. This could involve conducting a larger sample size or collecting data from multiple sources. Additionally, researchers could investigate the factors that contribute to the variation in recharge time, such as battery type or usage patterns.

Limitations

One limitation of this study is that it is based on a random sample of 50 company tablet computers. While this sample size is sufficient for hypothesis testing, it may not be representative of the entire population of tablet computers. Future research could involve collecting data from a larger sample size or using more advanced statistical methods to account for potential biases.

Conclusion

Introduction

In our previous article, we discussed a company's claim about its tablet computers, specifically their recharge time. We analyzed the data collected by a consumer group and determined that the company's claim is not reliable. In this article, we will answer some frequently asked questions (FAQs) about the study and its findings.

Q: What was the company's claim about its tablet computers?

A: The company claimed that its tablet computers have an average recharge time of 3 hours with a standard deviation of 1.4 hours.

Q: What was the sample size of the consumer group's study?

A: The consumer group collected data from a random sample of 50 company tablet computers.

Q: What was the mean recharge time of the sample?

A: The mean recharge time of the sample was 2.5 hours.

Q: What was the standard deviation of the sample?

A: The standard deviation of the sample was 1.2 hours.

Q: How did you determine that the company's claim is not reliable?

A: We performed a hypothesis test to determine if the mean recharge time of the company's tablet computers is equal to 3 hours. The p-value of the test was 0.001, which is very small, indicating that the observed difference between the sample mean and the population mean is statistically significant. Therefore, we can reject the null hypothesis and conclude that the mean recharge time of the company's tablet computers is not equal to 3 hours.

Q: What are the implications of this study?

A: The implications of this study are significant. Consumers who are considering purchasing the company's tablet computers should be aware of the actual recharge time, which is 2.5 hours. This information can help consumers make informed decisions about their purchases.

Q: What are some potential limitations of this study?

A: One limitation of this study is that it is based on a random sample of 50 company tablet computers. While this sample size is sufficient for hypothesis testing, it may not be representative of the entire population of tablet computers. Future research could involve collecting data from a larger sample size or using more advanced statistical methods to account for potential biases.

Q: What are some potential future research directions?

A: Future research could involve collecting more data on the recharge time of the company's tablet computers. This could involve conducting a larger sample size or collecting data from multiple sources. Additionally, researchers could investigate the factors that contribute to the variation in recharge time, such as battery type or usage patterns.

Q: How can consumers make informed decisions about their purchases?

A: Consumers can make informed decisions about their purchases by being aware of the actual recharge time of the company's tablet computers. They can also consider other factors, such as battery life, processing power, and storage capacity, when making their purchasing decisions.

Q: What are some potential consequences of the company's claim being unreliable?

A: The potential consequences of the company's claim being unreliable are significant. Consumers who purchase the company's tablet computers based on the claim may be disappointed with the actual recharge time, which could lead to a loss of trust in the company and its products.