Statistics level of significance

In summary, the conversation discusses the required sample sizes for conducting a two-sided one-sample t-test with a specific effect size, sample variance, and level of significance. The first question involves using the standard normal distribution and the second question involves using the binomial distribution. The third question is about the differences and similarities between the sample sizes required for the first two questions. The speaker admits to being confused and needing guidance on how to approach the problems.
  • #1
tedpark1212
14
0
I need help with these statistics problems. Can anyone guide me through them? I would greatly appreciate it. I am completely lost on where to start.

1. Suppose you want to show the significance of an effect size of 0.20 between your sample mean and a hypothesized mean. You intend to conduct a two-sided one-sample t-test. The sample variance is σ2 = 1.0. You assume that the population is large, or effectively infinite. If you want the test to have a power of 0.80, what is the required sample size for the following?

So for here I would use standard normal distribution, correct?

• A level of significance of α = 0.05


• A level of significance of α = 0.01



2. After some research, you determine that the size of the population is N = 350. If you want the test to have a power of 0.80, what is the required sample size for the following?

For question 2 I would use binominal distribution? I'm really confused on how to work the equations.

• A level of significance of α = 0.05


• A level of significance of α = 0.01


3. Comment on the sample sizes required for questions 3 and 4. Explain the differences and similarities.
 
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  • #2
tedpark1212 said:
I need help with these statistics problems. Can anyone guide me through them? I would greatly appreciate it. I am completely lost on where to start.

1. Suppose you want to show the significance of an effect size of 0.20 between your sample mean and a hypothesized mean. You intend to conduct a two-sided one-sample t-test. The sample variance is σ2 = 1.0. You assume that the population is large, or effectively infinite. If you want the test to have a power of 0.80, what is the required sample size for the following?

So for here I would use standard normal distribution, correct?

• A level of significance of α = 0.05


• A level of significance of α = 0.01



2. After some research, you determine that the size of the population is N = 350. If you want the test to have a power of 0.80, what is the required sample size for the following?

For question 2 I would use binominal distribution? I'm really confused on how to work the equations.

• A level of significance of α = 0.05


• A level of significance of α = 0.01


3. Comment on the sample sizes required for questions 3 and 4. Explain the differences and similarities.

PF rules require you to show some effort. What have you done on this so far?
 
  • #3
I have yet only established an idea of only which approach to use, but I am unable to implement it in my work.
 

Related to Statistics level of significance

1. What is the significance level in statistics?

The significance level, also known as alpha (α), is a threshold used in hypothesis testing to determine if the results of a statistical analysis are statistically significant. It is typically set at a value of 0.05 or 0.01, and represents the probability of making a Type I error (rejecting the null hypothesis when it is actually true).

2. How is the significance level chosen?

The significance level is chosen by the researcher based on the level of risk they are willing to accept for making a Type I error. A lower significance level (e.g. 0.01) reduces the chances of a false positive, but also increases the likelihood of a false negative. It is important to carefully consider the potential consequences and make an informed decision when selecting the significance level.

3. How is the significance level related to the p-value?

The significance level and p-value are both measures of statistical significance, but they are not the same. The significance level is a predetermined threshold used to determine if the p-value is low enough to reject the null hypothesis. The p-value is the probability of obtaining the observed results (or more extreme results) if the null hypothesis is true. If the p-value is less than or equal to the significance level, the results are considered statistically significant.

4. Can the significance level be changed during analysis?

No, the significance level should be determined before conducting the statistical analysis and should not be changed during the analysis. Changing the significance level after seeing the results can lead to biased or misleading conclusions.

5. What happens if the significance level is not met?

If the p-value is greater than the significance level, it means that the results are not statistically significant. This does not necessarily mean that the results are not meaningful, but rather that there is not enough evidence to reject the null hypothesis. In this case, the researcher may need to consider alternative explanations or collect more data to further investigate the phenomenon.

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