Stats Lab Homework Review
What is a type I error? What is a type II error?
(A type I error is the mistake of rejecting the null hypothesis when the null hypothesis is actually true.) Rejecting the null hypothesis, when it is true (A type II error is the mistake of failing to reject the null hypothesis when the null hypothesis is actually false.) Not rejecting the null hypothesis when it is false
What does the p-value mean?
A p-value is the probability of observing a value of a statistic or a value that is more unusual just by chance if the null hypothesis is true.
Is this statement true or false? If false, why? A p-value is the probability of observing a value of a statistic or a value that is more unusual just by chance.
False: A p-value is the probability of observing a value of a statistic or a value that is more unusual just by chance only if the null hypothesis is true.
What does a two-sided test is performed when the alternative hypothesis state?
That the parameter is not equal to the hypothesized value.
What is the difference between the t-distribution and the standard normal distribution?
the t-distribution has thicker tails than the standard normal distribution
What are the requirements for the Central Limit Theorem?
1) Random sampling and independent 2) Large population: 10 times larger than sample size 3)Large sample: (population distribution is normal or the sample size is at least 25)
What sample size is considered "large"
25 or more
What is a Type I error?
A Type I error results if the null hypothesis is rejected when, in fact, the null hypothesis is true.
What does a high p-value mean?
A high p-value indicates that there is not enough evidence to reject the null hypothesis. But, it doesn't mean the null hypothesis should be accepted as true.
What is a hypothesis in statistics?
A hypothesis is a claim about a population parameter (such as a population proportion, p, or a population mean, m, μ) or some other characteristic of a population.
What is meant by a hypothesis test in statistics?
A hypothesis test is a standard procedure for testing a claim about the value of a population parameter.
Why is the null hypothesis rejected when the p-value is small?
Because a lower p-value indicates that the sample data is more unusual.
When computing the t-statistic, one divides by an estimate of the standard error. Why not divide by the true standard error?
Because in real life, one almost never knows the value of the population standard deviation.
It is hypothesized that 50% of Americans attend church regularly. Which of the following would be an example of making a Type I Error? A.A study was conducted that failed to reject the null hypothesis. In reality, only 40% of Americans attend church regularly. B.A study was conducted that failed to reject the null hypothesis. In reality, half of Americans actually do attend church regularly. C.A study was conducted that had evidence to reject the null hypothesis. In reality, only 40% of Americans attend church regularly. D.A study was conducted that had evidence to reject the null hypothesis. In reality, half of Americans actually do attend church regularly.
D (A study was conducted that had evidence to reject the null hypothesis. In reality, half of Americans actually do attend church regularly.)
What should you do if... The P-value is greater than the level of significance
Do not reject the null hypothesis and conclude there is insufficient evidence to support the alternative hypothesis.
Is this statement true or false? Why? Researchers conducted a study and obtained a p-value of 0.30. Because the p-value is quite high, there is evidence to accept the null hypothesis.
False A high p-value indicates not enough evidence to reject the null hypothesis.
What should you do if... The P-value is equal to or less than the level of significance
Reject the null hypothesis and conclude there is sufficient evidence to support the alternative hypothesis.
The claim being assessed in a hypothesis test is called...
The null hypothesis
What is the mean of the sampling distribution of the sample mean?
The population mean
What is the P-Value and what does a smaller p-value mean?
The probability that the test statistic = the observed value or a more extreme value. Smaller p-value gives stronger evidence against the null hypothesis.
In a t-distribution, the degrees of freedom are related to...
The sample size
What is the significance level of a test?
The significance level is the probability of making the mistake of rejecting the null hypothesis even though it is true
Does this make sense? In testing a claim about a population mean, if the standard score for a sample mean is z=0, then there is not sufficient sample evidence to support the alternative hypothesis.
The statement makes sense. A standard score of 0 represents the peak of the sampling distribution, so it is a likely outcome if the null hypothesis is true.
What do p, p(hat) , and P-value represent?
The symbol p represents the proportion in a population, p(hat) represents the proportion in a sample, P-value is the probability of getting a sample proportion that is at least as extreme as the sample proportion actually observed given that the null hypothesis is true.
Does a P-value of 0.003 give strong evidence or not especially strong evidence against the null hypothesis?
The P-value gives strong evidence against the null hypothesis because it is small.
In hypothesis tests, if the significance level is 0.01, then the P-value is also 0.01.
The P-value is the probability of finding a sample statistic at least as extreme as the one found, under the assumption that the null hypothesis is true. A P-value can take on any value between 0 and 1 and is usually not equal to the level of significance chosen by the researcher.
Is this statement true? If not, why? A p-value is the probability that the null hypothesis is true.
This statement is false. The null hypothesis will either be true or it won't be true - there is no probability associated with this fact. A p-value is the probability of observing a sample mean (For Example - that we did or something more unusual just by chance if the null hypothesis is true.)
Is this statement true? If not, why? A p-value is the probability of accepting the null hypothesis.
This statement is false. We never accept the null hypothesis no matter what the p-value is. A p-value is the probability of observing a sample mean (for example) that we did or something more unusual just by chance if the null hypothesis is true.
Rejecting the null hypothesis when the null hypothesis is true is called...
a Type I Error (Alpha, or the significance level)
