Test 1 Stats
Alex hypothesized that students study less than the recommended two hours per credit hour each week outside of class. Alex performed a hypothesis test and told a colleague that he had evidence to indicate his hypothesis was true. Which of the following is a true statement that his colleague could have said? 1)Alex should never accept the null hypothesis as true. 2)There was no chance Alex could have made any error. 3)Alex might have made a Type I Error. 4)Alex might have made a Type II Error.
Alex might have made a Type 1 error.
A p-value is the probability _____________. Choose the correct answer below. 1)A p-value is the probability of observing the actual result, a sample mean, for example. 2)A p-value is the probability of observing the actual result, a sample mean, for example, or something more unusual just by chance if the null hypothesis is true. 3)A p-value is the probability that the null hypothesis is true. 4)A p-value is the probability of observing the actual result, a sample mean, for example, or something more unusual just by chance if the null hypothesis is false.
A p-value is the probability of observing the actual result, a sample mean, for example, or something more unusual just by chance if the null hypothesis is true.
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? 1)0.80 2)0.05 3)0.20 4)Type I Error cannot occur when the null hypothesis is rejected.
0.05
Power is 1)Power is the probability that a hypothesis test will correctly reject a false null hypothesis. 2)Power is failing to reject the null hypothesis when the null hypothesis is false. 3)Power is the probability of observing what we did or something more unusual just by chance if the null hypothesis is true. 4)Power is the probability that a hypothesis test will incorrectly reject the null hypothesis.
Power is probability that hypothesis test will correctly reject a false null hypothesis.
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? 1) judgement error 2) measurement error 3)Type II Error 4) Type I Error
Type 1 error
Before lending someone money, banks must decide whether they believe the applicant will repay the loan. One strategy used is a point system. Loan officers assess information about the applicant, totaling points they award for the person's income level, credit history, current debt burden, and so on. The higher the point total, the more convinced the bank is that it's safe to make the loan. Any applicant with a lower point total than a certain cutoff score is denied a loan. We can think of this decision as a hypothesis test. Since the bank makes its profit from the interest collected on repaid loans, their null hypothesis is that the applicant will repay the loan and therefore should get the money. Only if the person's score falls below the minimum cutoff will the bank reject the null and deny the loan. a) When a person defaults on a loan, which type of error did the bank make? Type I error Type II error b) Which kind of error is it when the bank misses an opportunity to make a loan to someone who would have repaid it? Type I error Type II error c) Suppose the bank decides to lower the cutoff score from 250 points to 200. Is that analogous to choosing a higher or lower value of alphaα for a hypothesis test? lower alpha level higher alpha level d) What impact does this change in the cutoff value have on the chance of each type of error? Increased Type I, increased Type II Increased Type I, decreased Type II. Decreased Type I, decreased Type II. Decreased Type I, increased Type II.
a) Type II error b) Type I error c) lower alpha level d) Decreased type I, Increased Type II
A company is sued for job discrimination because only 13% of the newly hired candidates were immigrants when 45% of all applicants were immigrants. a) In this context, what would a Type I error be? 1) A Type I error is deciding the company is discriminating when, in fact, it is. 2) A Type I error is deciding the company is not discriminating when, in fact, it is not. 3) A Type I error is deciding the company is not discriminating when it is. 4) A Type I error is deciding the company is discriminating when it is not. 5) There is no Type I error in this context b)In this context, what would a Type II error be? 1) A Type II error is deciding the company is not discriminating when, in fact, it is not. 2) A Type II error is deciding the company is discriminating when, in fact, it is. 3) A Type II error is deciding the company is not discriminating when it is. 4) A Type II error is deciding the company is discriminating when it is not. 5) There is no Type II error in this context. c)If the hypothesis is tested at the 10% level of significance instead of 1%, how will this affect the power of the test? 1)The power of the test will increase because the level of significance decreased. 2)The power of the test will decrease because the level of significance increased.. 3)The power of the test will increase because the level of significance increased. 4)The power of the test will decrease because the level of significance decreased. d) The lawsuit is based on the hiring of 46 employees. Is the power of the test higher than, lower than, or the same as it would be if it were based on 91 hires? 1) The power of the test is higher because the sample size decreases. 2) The power of the test is lower because the sample size decreases. 3) The power of the test is the same regardless of the change in sample size.
a) Type I error is deciding the company is discriminating when it is not. b) Type II error is deciding company is not discriminating when it is. c) The power of test will increase because the level of significance increased. d) The power of the test is lower because the sample size decreases.
It is hypothesized that 50% of Americans attend church regularly. Which of the following would be an example of making a Type I Error? 1)A study was conducted that had evidence to reject the null hypothesis. In reality, half of Americans actually do attend church regularly. 2)A study was conducted that had evidence to reject the null hypothesis. In reality, only 40% of Americans attend church regularly. 3)A study was conducted that failed to reject the null hypothesis. In reality, half of Americans actually do attend church regularly. 4)A study was conducted that failed to reject the null hypothesis. In reality, only 40% of Americans attend church regularly.
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 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? 1)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. 2)Cameron had 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 no difference in the average scores. 3) 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, and there really was no difference in the average scores. 4) Cameron had 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, and there really was a difference in the average scores.
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.
Researchers conducted a study and obtained a p-value of 0.75. Based on this p-value, what conclusion should the researchers draw? Choose the correct answer below. 1)Redo the study as it is not possible to get a p-value that high. 2)Fail to reject the null hypothesis but do not accept the null hypothesis as true either. 3)Reject the null hypothesis and accept the alternative as true. 4)Reject the null hypothesis but do not accept the alternative as true. 5)Fail to reject the null hypothesis and, therefore, accept the null hypothesis as true.
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 cell phone. Which of the following would be an example of researchers making a Type II Error? 1) From a study conducted, researchers failed to reject their null hypothesis. In fact 85% of Americans own cell phones. 2) From a study conducted, researchers had evidence to reject their null hypothesis. In fact 85% of Americans own cell phones. 3) From a study conducted, researchers failed to reject their null hypothesis. In fact 90% of Americans own cell phones. 4) From a study conducted, researchers had evidence to reject their null hypothesis. In fact 90% of Americans own cell phones.
From a study conducted, researchers failed to reject their null hypothesis. In fact 90% of Americans own cell phones.
Eric randomly surveyed 150 adults from a certain city and asked which team in a contest they were rooting for, either North High School or South High School. Of the surveyed adults, 96 said they were rooting for North High while the rest said they were rooting for South High. Eric wants to determine if this is evidence that more than half the adults in this city will root for North High School. Suppose a p-value from the correct hypothesis test was 0.0030. Which of the following is a correct interpretation of this p-value? 1)If more than half of all adults in this city root for North High, 3 out of every 1000 random samples of the same size from this population would produce the same result observed in this study or a result more unusual. 2)If half of all adults in this city root for North High, 3 out of every 1000 random samples of the same size from this population would produce the same result observed in this study or a result more unusual. 3)It states that 3 out of every 1000 random samples of the same size from this population would produce the same result observed in this study or a result more unusual. 4)There's a 0.3% chance that the null hypothesis is true.
If half of all students in this city root for North High, 3 out of every 1000 random samples of same size from this population would produce same results observed in this study or result more unusual.
Allison randomly sampled 40 students in a particular class and asked each how many hours per week they studied. She calculated a sample mean of 9.5 hours per week. Her hypotheses were HO: sample mean symbol =8 hours per week and HA: sample mean symbol >8 hours per week, where x is the number of hours students spent studying per week. She performed a hypothesis test and obtained a p-value of 0.0003. What does this mean? 1)Of all the random samples of 40 students from this class, 0.03% would give a sample mean of 9.5 hours per week or more given that the true mean number of hours spent studying for this class for all students in the class is 8 hours per week. 2)The probability that the mean number of hours spent studying per week for all students in this class is more than 8 hours per week is 0.0003. 3)The probability that the mean number of hours spent studying per week for all students in this class is 8 hours per week is 0.0003. 4)The probability that the true mean number of hours spent studying per week for all students in this class is 9.5 hours or more is 0.0003.
Of all the random samples of 40 students from this class, 0.03% would give a sample mean of 9.5 hours per week or more given that the true mean of hours spent studying for this class for all students in the class is hours per week.
Researchers wondered if the average water temperature of streams without tailed frogs was different than the average water temperature of streams with tailed frogs, which is known to be 12.2 degrees Celsius. A survey of 31 streams without tailed frogs was taken and the water temperature was recorded for each stream. Which of the following is the correct statement of what a Type I Error is in the context of this problem? 1)Researchers found evidence that the average water temperature of streams without tailed frogs was different than the average water temperature of streams with tailed frogs when there was no difference in the average temperatures. 2)Researchers found no evidence that the average water temperature of streams without tailed frogs was different than the average water temperature of streams with tailed frogs and there really was no difference in the average temperatures. 3)Researchers found no evidence that the average water temperature of streams without tailed frogs was different than the average water temperature of streams with tailed frogs when there was a difference in the average temperatures. 4)Researchers found evidence that the average water temperature of streams without tailed frogs was different than the average water temperature of streams with tailed frogs and there really was a difference in the average temperatures.
Researchers found evidence that the average water temperature of streams without tailed frogs was different than the average water temperature of streams with tailed frogs when there was no difference in the average temperatures.
A medical study was investigating if getting a flu shot actually reduced the risk of developing the flu. A hypothesis test is performed. Which of the following will result in a Type 1 error? 1)Researchers said the flu shot did not reduce the risk of developing the flu when it actually didn't. 2)Researchers said the flu shot reduced the risk of developing the flu when it actually did. 3)Researchers said the flu shot reduced the risk of developing the flu when it actually didn't. 4)Researchers could not tell if the flu shot reduced the risk of developing the flu because of other problems with the study. 5)Researchers said the flu shot did not reduce the risk of developing the flu when it actually did.
Researchers said the flu shot reduced the risk of developing the flu when it actually didn't.
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 found no evidence to reject the null hypothesis at the 5% significance level. What is true regarding the p-value from this hypothesis test? Choose the correct answer below. 1)The p-value must have been greater than 0.05. 2)The p-value must have been less than or equal to 0.05. 3)The p-value must have been equal to 0.05. 4)We cannot determine a range for the p-value based on the information given.
The p-value must have been greater than 0.05.
Is the average body temperature of humans really 98.6degrees°F? After sampling 15,600 healthy people from around the country, researchers found a sample mean of 98.5degrees°F. The p-value was 0.0001. Which of the following is true? Choose the correct answer below. 1)The results are not "statistically significant" because the sample size was not large enough. 2)The results are not "statistically significant" because the difference between the sample mean and the hypothesized value was not large. 3)The results are "statistically significant" because the standard deviation from the population of all humans is probably very large. D. The results are "statistically significant" because the people in the sample are healthy. E. The results are "statistically significant" because the sample size was quite large and the p-value was quite small.
The results are statistically significant because the sample size was quite large and the p -value was quite small.
Alex hypothesized that, on average, students study less than the recommended two hours per credit hour each week outside of class. Alex performed a hypothesis test and obtained a p-value of 0.01. Assuming all conditions are met, which of the following is the most appropriate conclusion? 1)There is evidence to indicate students study less than the recommended two hours per credit hour each week, on average. 2)There is not enough evidence to indicate students study the recommended two hours per credit hour each week, on average. 3)There is evidence to indicate students study the recommended two hours per credit hour each week, on average. 4)There is evidence to indicate all students study less than the recommended two hours per credit hour each week.
There is evidence to indicate students study less than the recommended two hours per credit hour each week, on average.
A type II error is made when 1) Type II Error is made anytime we do not reject the null hypothesis. 2)Type II Error is made when there's not enough evidence to reject the null hypothesis and the null hypothesis is true. 3)Type II Error is made when there's not enough evidence to reject the null hypothesis, but the null hypothesis is not true. 4)Type II Error is made when there's evidence to reject the null hypothesis, but the null hypothesis is true.
Type II error is made when there's not enough evidence to reject the null hypothesis, but the null hypothesis is not true.
