Stats Class Hypothesis Theory Quiz
John sets up a one sample z-test for proportions with a significance level of 0.05. He then performs the test and rejects the null hypothesis. The probability he correctly rejected the null hypothesis is 0.80. What is the probability of a Type I Error occurring?
0.05
Describe a Paired T-Test?
A PAIRED T-TEST is a one sample T-Test On THE MEANS of THE OBSERVATIONS IN THE 2 GROUPS.
Describe a T-test.
A paired t- test is a one sample t-test on the differences of the observations in the two groups.
Describe a PAIRED T-TEST.
A paired t-test is a one sample t test on the differences of the observations in the two groups.
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 study was conducted that had evidence to reject the null hypothesis. In reality, half of Americans ACTUALLY DO ATTEND CHURCH REGULARLY.
Cameron wondered if the average score on a final exam was different between those who texted on a regular basis during lecture for a particular class and those that did not text at all. Which of the following is the correct statement of what a Type II Error is in the context of this problem.
Cameron did not have evidence that there was a difference in the average scores on the final exam between those who texted during lecture and those who did not text during lecture when there was a difference in the average scores.
Cameron wondered if the average score on a final exam was different between those who texted on a regular basis during lecture for the same class. Which of the following is the correct statement of what a Type II Error is in the context of this problem?
Cameron did not have evidence that there was a difference in the average scores on the final exam between those who texted during lecture and those who did not text during lecture when there was a difference in the average scores.
A student was wondering if students at her university arrived on campus each day the same way as another university. At the other university, 60% drove, 30% rode a bike or walked, and the other 10% arrived using other means of transportation. The STUDENT RANDOMLY SAMPLED 150 students one afternoon at her university and asked how they arrived at campus that day. Which hypothesis test should the student use to determine if students at her university arrive to campus in the same proportion as the other university?
Chi square goodness of fit test.
A voter was interested in comparing the proportion in favor of national health care between people who say they are REPUBLICANS, DEMOCRATS, AND INDEPDENDENTS. From each party, she RANDOMLY selected 50 people registered as a member of that party in her county and asked whether or not they were in favor of a national health care program. Which of the following hypothesis tests should this voter use?
Chi-Square test of Homogeneity.
Nurses knew that the average birth weight of a baby last year was 7.6 lbs. A RANDOM SAMPLE of 15 weights of babies at the hospital gave an AVERGE BIRTH WEIGHT OF 7.9 lbs. Nurses felt that the birth weights this year were normally distributed. WHICH OF THE FOLLOWING IS TRUE ABOUT THE DISTRIBUTION OF SAMPLE MEANS?
Even though the sample size is LESS THAN 30, THE DISTRIBUTION OF SAMPLE MEANS will be NORMAL BECAUSE the population data follow a NORMAL DISTRIBUTION.
Researchers conducted a study and obtained a p-value of 0.75. Based on this p-value, what conclusion should the researchers draw?
Fail to reject the null hypothesis but do not accept the null hypothesis as true either.
A researcher hypothesizes more than 85% of Americans own a cellphone. Which of the following would be an example of researchers making a Type II Error?
From a study conducted, researchers failed to reject their null hypothesis. In fact, 90% of Americans own cell phones.
Alex hypothesized that students study LESS THAN the recommended 2 hours per credit each week outside of class. Alex performed a hypothesis test and told a friend that he had evidence to INDICICATE his hypothesis was true. Which of the following is a true statement that his friend could have said?
He MIGHT HAVE MADE a Type I Error.
suppose x=60. Ho: u=50, Hi: u>50, and the p-value from a one sample test is 0.04. What does this p value mean?
The probability of getting a sample mean of 60 or more if the true population mean is 50 is 0.04.
A student wondered if more than 10% of students enrolled in an introductory Chemistry class dropped before the midterm. He noticed that 2 OUT OF 15 of his friends in the class DROPPED BEFORE the midterm. Based on his sample, he performed a hypothesis test. Is the hypothesis test a one tailed or two tailed test?
ITS IS A ONE TAILED TEST since the alternative Hypothesis states that the parameter is GREATER THAN the hypothesized value.
Power is ____________.
Is the probability that a hypothesis test will correctly reject a false null hypothesis.
A P-Value is the probability ____.
The probability of observing the actual result, a sample mean, for example, or something more UNUSUAL JUST BE CHANCE IF THE NULL HYPOTHESIS IS **TRUE**
a ONE-SAMPLE TEST is to be performed. Researchers are wondering if the normality condition is met. The normal probability plot below was constructed based on data collected on GPAs from a RANDOM SAMPLE OF COLLEGE STUDENTS. BASED ON THE NORMAL PROBABILITY PLOT, WHICH OF THE FOLLOWING STATEMENTS IS CORRECT?
Since the sample data do not appear to be normally distributed and since a random sample was taken, IT CANNOT BE SAID THAT GPA'S of all college students follow a normal distribution.
Researchers timed 21 subjects as they tried to complete paper and pencil mazes. Each subject attempted a maze both with and without the presence of a floral aroma. subjects were randomized with respect to which trial they did first. suppose a paired t test is to be performed to determine whether there is evidence to indicate that the time to complete the maze is faster in scented trials compared to unscented trials on average. The P_Value from the paired t-test is 0.11. Which of the following is the most appropriate conclusion based on this p-value?
THERE IS NOT SUFFICIENT EVIDENCE TO INDICATE that the individuals complete mazes faster with a floral aroma present compared to when no floral aroma is present on average.
Doug wondered how students felt about a student fee increase. he randomly sampled 100 freshmen, 100 sophmores, 100 juniors, and 100 seniors at his university. He asked each whether or not they supported the fee increase. Assuming all conditions are satisfied, which test should Doug use to test the hypothesis that the distribution is the same for all 4 classes?
The Goodness Of Fit Homogeneity
Dora likes to explore. She recently discovered trees known as Eucalyptus Regnans aka Fountain Ash. She wondred if they were, ON AVERAGE, THAN THE DOUGLAS FIRS, Which have an average height of 250 feet in old growth areas. Dora measured the heights of 15 Mountain Ash trees and found an average height of these trees are 293 feet. Suppose s= 25 feet. Assume the heights of the 15 trees in Dora's sample are representative of the heights of all Mountain Ash trees. Which hypothesis test should be used?
The ONE SAMPLE T- TEST
Its recommended that adults get 8 hours of sleep each night. a researcher hypothesized college students got less than the recommended number of hours of sleep each night, on average. The researcher RANDOMLY SAMPLED 20 COLLEGE SUDENTS and FOUND NO EVIDENCE TO REJECT the null hypothesis at the 5% significance level. What is true regarding the p-value from this hypothesis test?
The P-Value must have been greater than 0.05.
A study was conducted on a sample size of 30 individuals. The P-value was 0.10. Suppose a researcher conducted another study by taking a random sample of 50 individuals from the same sample population. Suppose they obtained the same sample mean as in the first study with a sample size of 30. (Also assume the population standard deviation is the same for both studies.) Which of the following is true?
The P-Value would be smaller for the second study.
Brett is a huge sports fan. he randomly sampled 500 American sports fans and asked each what was their fave sport and what part of the country did they live in. Assuming all conditions are satisfied, which of the following tests should Brett use to test his hypothesis?
The chi square test of independence.
It is recommended that adults get 8 hours of sleep each night. A researcher hypothesized college students got less than the recommended number of hours of sleep each night on average. The researcher randomly sampled 20 college students and calculated a sample mean of 7.5 hours per night. If the researcher wanted to perform a one sample t-test, which of the following is a correct statement?
The number of hours of sleep per night for all college students must be normally distributed because the sample size is small.
Is the AVERAGE body temperature of humans really 98.6 degrees. After sampling 15,600 healthy people from around the country, researchers found a SAMPLE MEAN OF 98.5 DEGREES F. The p-vale was 0.0001. Which of the following is true?
The results are "STATISTICALLY SIGNIFICANT" Because the SAMPLE SIZE WAS QUITE LARGE and the P-VALUE WAS QUITE SMALL.
What does the standard deviation error of the distribution of sample means estimate?
The standard deviation of the distribution of sample means.
Clifford likes dogs and wonders how much owners spend on their dogs in a year. He hypothesized that dog owners spend more than $1,000 a year on their dogs on average. he sampled 75 dog owners in a year. Suppose ox=$175. Assume that these 75 dog owners are representative of all dog owners in terms of amount spent on their dogs in a year. The p-value of 0.0001. What conclusion should be made?
There IS STRONG EVIDENCE that all dog owners spend more than $1000 on their dogs each year on average.
Elmo likes music. He wondered if listening to music while studying will improve scores on an exam. 50 students who were to take the midterm in a week agreed to be part of a study. Half were randomly assigned to listen to classical music while studying for the exam. A Hypothesis test is to be performed to determine if the average score of those listening to music while studying for the exam was higher than for those who did not listen to any music while studying for the exam. Which of the following is the correct null hypothesis?
There is NO DIFFERENCE IN THE MEAN MIDTERM scores between those who listen to classical music while studying AND those who DONT listen to music while studying.
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.
John performed a one sample Z-Test for Proportions and rejected the null hypothesis at a significance level of 0.05. What type of error could John have made with his conclusion?
Type I Error
when are conclusions said to be "STATISTICALLY SIGNIFICANT?"
When the P-VALUE is LESS THAN a GIVEN SIGNIFICANCE LEVEL.
In a paired t-test, when will the distribution of sample means of the differences be normal or approximately normal?
When the sample size is at least 30 and when the distribution of differences in the population is normal.
WHEN WILL a chi square statistic BE ZERO?
when all observed counts are the same as their expected counts.
What are conclusions said to be "statistically significant"?
when the P-value is less than a given significance level.
