‘Children can learn a second language faster before the age of 7’. Is this statement:
- A one-tailed hypothesis
- A non-scientific statement
- A two-tailed hypothesis
- A null hypothesis
A one-tailed hypothesis
The statement implies a directional hypothesis (children can learn faster before the age of 7), which aligns with a one-tailed hypothesis.
Which of the following is true about a 95% confidence interval of the mean?
- 95 out of 100 sample means will fall within the limits of the confidence interval.
- There is a 0.05 probability that the population mean falls within the limits of the confidence interval.
- 95 out of 100 confidence intervals will contain the population mean.
- 95% of population means will fall within the limits of the confidence interval.
95 out of 100 confidence intervals will contain the population mean
What does a significant test statistic tell us?
1. There is an important effect.
2. The null hypothesis is false.
3. That the test statistic is larger than we would expect if there were no effect in the population.
4. All of the above.
That the test statistic is larger than we would expect if there were no effect in the population.
A type 1 error occurs when:
1. We conclude that there is not an effect in the population when in fact there is.
2. We conclude that the test statistic is significant when in fact it is not.
3. We conclude that there is an effect in the population when in fact there is not.
4. The data we have typed into SPSS is different from the data collected.
We conclude that there is an effect in the population when in fact there is not.
Power is the ability of a test to detect an effect given that an effect of a certain size exists in a population.
- True
- False
True
We can use power to determine how large a sample is required to detect an effect of a certain size.
- True
- False
True
Statistical power is the probability that a test will correctly reject a false null hypothesis. It is used in sample size calculations to determine how large a sample is needed to detect a specified effect size with a desired level of power.
Power is linked to the probability of making a Type II error.
- True
- False
True
The power of a test is the probability that a given test is reliable and valid.
1. True
2. False
False
The power of a test is the probability of correctly rejecting a false null hypothesis. Reliability and validity are terms more associated with the quality of measurement instruments.
What is the relationship between sample size and the standard error of the mean?
- The standard error increases as the sample size increases.
- The standard error decreases as the sample size decreases.
- The standard error decreases as the sample size increases.
- The standard error is unaffected by the sample size.
The standard error decreases as the sample size increases.
What is the null hypothesis for the following question: Is there a relationship between heart rate and the number of cups of coffee drunk within the last 4 hours?
- There will be no relationship between heart rate and the number of cups of coffee drunk within the last 4 hours.
- People who drink more coffee will have significantly higher heart rates.
- People who drink more cups of coffee will have significantly lower heart rates.
- There will be a significant relationship between the number of cups of coffee drunk within the last 4 hours and heart rate.
There will be no relationship between heart rate and the number of cups of coffee drunk within the last 4 hours.
A Type II error occurs when:
1. The data we have typed into SPSS is different from the data collected.
2. We conclude that the test statistic is significant when in fact it is not.
3. We conclude that there is an effect in the population when in fact there is not.
4. We conclude that there is not an effect in the population when in fact there is.
We conclude that there is not an effect in the population when in fact there is.
In general, as the sample size (N) increases:
1. The confidence interval becomes less accurate.
2. The confidence interval gets wider.
3. The confidence interval gets narrower.
4. The confidence interval is unaffected.
The confidence interval gets narrower.
As the sample size increases, the precision of the estimate improves, leading to a narrower confidence interval.
Which of the following best describes the relationship between sample size and significance testing?
1. In small samples only small effects will be deemed ‘significant’.
2. In large samples even small effects can be deemed ‘significant’.
3. Large effects tend to be significant only in small samples.
4. Large effects tend to be significant only in large samples.
In large samples even small effects can be deemed ‘significant’.
In large samples, statistical tests may have more power to detect smaller effects, potentially leading to ‘statistical significance.’
The assumption of homogeneity of variance is met when:
1. The variances in different groups are significantly different
2. The variance is the same as the interquartile range
3. The variances in different groups are approximately equal
4. The variance across groups is proportional to the means of those groups
The variances in different groups are approximately equal.
Homogeneity of variance assumes that the variances across different groups are roughly equal, contributing to the validity of statistical tests like ANOVA.
Of what is p the probability?
- p is the probability that the results are due to chance, the probability that the null hypothesis (H0) is true.
- p is the probability that the results are not due to chance, the probability that the null hypothesis (H0) is false.
- p is the probability that the results would be replicated if the experiment was conducted a second time.
- p is the probability of observing a test statistic is at least as big as the one we have if there were no effect in the population (i.e., the null hypothesis were true)
p is the probability of observing a test statistic at least as extreme as the one we have if there were no effect in the population (i.e., the null hypothesis were true).
In hypothesis testing, the p-value (p) represents the probability of obtaining a test statistic as extreme as the one observed, assuming that the null hypothesis (H0) is true. A small p-value suggests that the observed results are unlikely to have occurred by chance alone, leading to the rejection of the null hypothesis. Therefore, option D accurately describes the interpretation of the p-value in the context of hypothesis testing.
