Inference for Means
In a paired t-test, this is what makes data “paired.”
What is the data are taken from the same or matched subjects?
This type of chi-square test is used to determine if a single categorical variable’s observed distribution matches a hypothesized distribution
What is a Chi-Square Goodness-of-Fit test?
In hypothesis testing, this type of error occurs when we reject a null hypothesis that is actually true.
What is a Type I error?
A hospital wants to see if a new drug can improve lung capacity. The hospital selects a random sample of 200 volunteers who smoke. Half of the smokers are randomly assigned to take the drug. The other half of smokers are assigned to take this typical option, which is usually a control for medical experiments.
What is a placebo?
The type of test that should be used when a student collects two independent samples to compare average sleep hours between students in AP Stats and AP Bio.
What is a two-sample t-test for the difference in means?
When calculating the chi square statistic how many times does the variable E and O appear.
What is 1 O and 2 E’s?
Ex: (o-e)^2/e
In a medical trial, a new drug is tested and the researchers fail to reject the null hypothesis, even though the drug is actually effective.
What is a Type II error?
A group of college students wants to study the effect of listening to music at different volumes while studying for a test. They found 100 volunteers, and assigned each volunteer a number from 1 to 100. They used a random number generator to assign the first 50 volunteers selected to study with quiet music. The remaining 50 volunteers are assigned to study with a loud volume. The experiment described above uses this allocation for the subjects.
What is a completely randomized assignment of subjects?
This is the condition that must be met if the population distribution is not known to be normal when constructing a confidence interval for a population mean.
What is the sample size must be large (n ≥ 30)?
A researcher conducts a Chi-Square Goodness-of-Fit test for a discrete probability distribution. After calculating the test statistic, they find it to be exactly zero. What does a chi-square statistic of zero imply about the observed data.
What is the observed counts exactly match the expected counts for every category?
This is one way to increase the power of a statistical test.
What is increasing the sample size or increasing the significance level?
Marta teaches physics. She has 2 versions of the final for her students, and wants to see if one version is harder. She has about 80 students in 4 different grade levels. She randomly assigns 50% of the students in each grade to each version. Marta then tests the average scores to see if they are significantly different. The experimental design Marta uses is called this.
What is a randomized block design (with 4 blocks)?
The conclusion that can be drawn from a 95% confidence interval for the difference in mean test scores of two different teaching methods. The range of the confidence interval is (−1, 4).
What is that there is no significant difference because the interval includes 0?
A national health organization has collected data on 100 adults from each of four distinct geographic regions, classifying each individual by their preferred way of staying informed about the news. The organization is interested in determining if the distribution of preferred methods of staying informed is the same across these four regions.
What is a Chi-Square Test of Homogeneity?
The error type that occurred when Gio took a pregnancy test and had a positive result.
What is type 1 error?
A grocery store wants to study whether offering free coupons for vegetables increases average shopping revenue. They select a random sample of 300 of their customers. They use a random number generator to select 150 customers to offer the coupons to. The remaining 150 customers are assigned to the control group. The grocery store uses this type of design.
What is a completely randomized design?
This is the primary reason we use a t-distribution instead of a z-distribution when performing inference for means.
What is the population standard deviation is unknown (and we are estimating it with the sample standard deviation)?
A medical researcher has obtained a single random sample of 1000 patients, categorizing each by their smoking status (Non-smoker, Former Smoker, Current Smoker) and the presence or absence of a lung condition. The researcher aims to investigate whether there is an association or relationship between a patient's smoking status and the occurrence of this lung condition.
What is a Chi-Square Test of Independence?
A researcher wants to decrease the probability of a Type I error. Doing this has this effect on the power of the test.
What is that it may decrease the power, because lowering alpha makes it harder to reject the null, increasing the chance of a Type II error?
Researchers working on a rash medicine collect a sample of 20,000 volunteers who are affected by the rash. Each volunteer was randomly assigned to receive the medicine for the rash or a placebo for 12 months. After the 12-month period, a doctor evaluates the effect of the medicine. The experimental design is double-blinded for this reason.
What is to minimize bias with the volunteer and doctor evaluating the rash?