Lecture 2 and 3 Flashcards
Why do we collect or analyse a sample for inferential statistics? Why not study the whole
population?
- To make inferences about a population based on information collected from a sample of that population.
- The cost and time efficiency, precision etc.
- What is the z-score in the standard normal distribution? What does it measure?
- It standardizes data and allows for meaningful comparisons across different normal distributions.
. Interpret the formula for z-score; 𝑧 =
𝑥̅−𝜇
𝜎/√𝑛
. What are the numerator and denominator
measuring? What does the z-score tell us about the sample mean, say if the value of z=1.5
or z=2?
Z= z-score, X is the sample mean, u is the population mean, sigma is the population standard deviation, n is the sample size
- Numerator is the part that measures the difference between sample mean and the population mean, it tells you how far the sample mean is from the expected population mean.
- Denominator, this part measures the standard error of the sample mean. It tells you how much the sample mean is expected to vary from sample to sample due to random sampling
- The z-score measures how many standard errors the sample mean is away from the population mean
- What are the steps in hypothesis testing?
State the null-hypothesis
- State the alternative-hypothesis
- Select a significance level
- Collect data and calculate test statistics, use t-test or chi-squared test.
- Determine the critical region
- compare the test statistic to critical region, can you reject the null-hypothesis
- interpret the result
- What is null hypothesis and alternative hypothesis? Give an example.
The null hypothesis states that there is no relationship in the population
- The alternative hypythesis is the statement you want to test.
- example:
The null-hypothesis: the new drug has no effect on blood pressure
The alternative hypothesis: The new drug significantly reduces blood pressure
Can you describe when to use what type of test (e.g., two-tailed, left-tailed, right-tailed)
for testing a hypothesis?
- For a two-tailed test: H1: μ ≠ μ0 (indicating a significant difference, with no specific direction).
- For a right-tailed test: H1: μ > μ0 (indicating a significant increase or positive effect).
- For a left-tailed test: H1: μ < μ0 (indicating a significant decrease or negative effect).
Write down an example for a null and two-sided alternative hypothesis.
H0: The mean weight of apples is equal to 150 grams (μ = 150).
H1: The mean weight of apples is not equal to 150 grams (μ ≠ 150). the sign is a not equal to
Write down an example for a null and one-sided alternative hypothesis.
H0: The mean height of the plant under specific conditions is equal to 30 centimeters (μ = 30).
H1: The mean height of the plant under specific conditions is greater than 30 centimeters (μ > 30).
Explain Type I and Type II errors. Provide an example.
- A Type I error occurs when you reject a null hypothesis that is actually true.
- In medical testing, a Type I error would occur if a healthy person is incorrectly diagnosed with a disease.
- A Type II error occurs when you fail to reject a null hypothesis that is actually false.
- In a criminal trial, a Type II error would occur if an innocent person is not acquitted(frikendt)
What is a confidence interval?
that provides a range of values, along with a level of confidence,
Confidence Interval=Xˉ±Z⋅√nσ
Where:
*ˉXˉ is the sample mean.
*Z is the critical value from the standard normal distribution associated with the chosen confidence level.
*σ is the population standard deviation (or the sample standard deviation if it’s a sample-based confidence interval).
*n is the sample size.
What is the p-value test? Based on the p-value, how would reject or fail to reject the null
hypothesis.
- Low P-value: A small p-value (typically less than the chosen significance level, α) suggests that the observed results are unlikely to have occurred by random chance alone. In this case, you reject the null hypothesis.
- High P-value: A large p-value suggests that the observed results are likely to occur by random chance, and there is insufficient evidence to reject the null hypothesis. In this case, you fail to reject the null hypothesis.
What is the significance level 𝛼 (alpha)? What is the relationship between 𝛼 and
confidence level?
- A significance level of α = 0.05 corresponds to a 95% confidence level.
- A significance level of α = 0.01 corresponds to a 99% confidence level.
If you were to design a study or analyse a dataset, which level of 𝛼 would you choose,
and why?
- I will have chosen the significance level of 95% because only the medicin industry are using the 99% significance level because the need to be sure that there product is working. And the 95% significance level is quiet normal to use in other situations.
If the p-value of the statistical analysis is less than 0.01 (or 0.05, 0.1), what does that say
about the statistical significance of the result?
- If the p-value is less of 0,01, there is a strong evidence that we can reject our null-hypothesis.
If the p-value of the statistical analysis is higher than 0.1, what does that say about the
statistical significance of the result?
If the p-value of the statistical analysis is higher than 0.1, the result are likely to occurred by random chance alone, which means we can not reject the null-hypotheses.
