STAT 100 Final
Is the given percent a statistic or a parameter? 75% of all students at a school are in favor of more bicycle parking spaces on campus. a. Statistic b. Parameter
b Since the percent refers to the population (i.e. all students) it is a parameter.
Assume that two sample means are 10.0 and 20.0, and the corresponding SEMs are 3.0 and 4.0. What is the Standard Deviation of the Difference in sample means (i.e. the SEM)? a. 25 b. √7 c. 5 d. 10
c We find the SEM of the difference by taking the square root of the sum of the square of each individual SEM, 32 plus 42 equals 25 and the square root of 25 is 5
Which statement is true about x-bar and p-hat? a. They are both statistics. b. They are both parameters. c. p-hat is a parameter and x-bar is a statistic. d. x-bar is a parameter and p-hat is a statistic.
a
In hypothesis testing, a Type 2 error occurs when a the null hypothesis is not rejected when the alternative hypothesis is true. b the null hypothesis is rejected when the null hypothesis is true. c the null hypothesis is not rejected when the null hypothesis is true. d the null hypothesis is rejected when the alternative hypothesis is true.
a A Type 2 error happens when a null hypothesis that is actually false is not rejected.
In a survey of n = 200 randomly selected individuals, 17% answered yes to the question "Do you think the use of marijuana should be made legal or not?" A 90% confidence interval for the proportion of all Americans in favor of legalizing marijuana is a. 0.17 ± 1.65 x 0.03 b. 0.17 ± 2.58 x 0.03 c. 0.17 ± 1.96 x 0.03 d. 0.17 ± 0.03
a A confidence interval is found by sample statistic multiplier*StandardError. With p-hat of 0.17, multiplier of 1.65 and n = 200, the 90% confidence interval is 0.17 1.65 x 0.03
Which of the following statements best describes the relationship between a parameter and a statistic? a. A statistic is used to estimate a parameter. b. A parameter is used to estimate a statistic.
a An underlying theme of statistics is to use statistics to estimate a parameter.
Determine if the statement is a typical null hypothesis (Ho) or alternative hypothesis (Ha). The average price of a particular statistics textbook over the internet is the same as the average price of the textbook sold at all bookstores in a college town. a Null hypothesis b Alternative hypothesis
a Ho refers to no difference or change or equal to. Ha will be the research hypothesis that involves either a difference, greater than, or less than.
Determine if the statement is a typical null hypothesis (Ho) or alternative hypothesis (Ha). The average time to graduate for undergraduate English majors is less than the average time to graduate for undergraduate history majors. a Alternative hypothesis b Null hypothesis
a Ho refers to no difference or change or equal to. Ha will be the research hypothesis that involves either a difference, greater than, or less than.
Determine if the statement is a typical null hypothesis (Ho) or alternative hypothesis (Ha). There is no difference between the proportion of overweight men and overweight women in America. a Null hypothesis b Alternative hypothesis
a Ho refers to no difference or change or equal to. Ha will be the research hypothesis that involves either a difference, greater than, or less than.
According to our lecture discussions, we stated that detecting a true difference when conducting an hypothesis test is easier (i.e. more likely) when the sample size is: a large b small
a Larger sample sizes make detecting differences more likely.
In the survey of a random sample of students at a university, two questions asked were "How many hours per week do you usually study?" and "Have you smoked marijuana in the past six months?" An analysis of the results comparing mean hours of study between those who did not smoke marijuana in the past six months to those who did (i.e. not smoked minus smoked) produced the following 95% confidence interval for this difference: 0.69 to 5.55 Based on this interval, what conclusion can be made about the difference in mean time spent studying between these two groups? a. Students that did not smoke marijuana in the past six months studied, on average, more hours per week than those who did smoke. b. We cannot say that there is a difference in mean study hours between the two groups. c. It is impossible to know if there is a difference because no p-value is provided.
a Since the 95% confidence interval does not contain 0 we could conclude that there is a difference in mean study hours and since the interval is positive and we took Not Smoke minus Smoke we can say that the non-smoking group on average studied more hours per week.
A hypothesis test was completed for an alternative hypothesis of Ha: p > 0.20 resulting in a test statistic of 1.41 From Table 8.1 what is the p-value for this test? a 0.08 b 0.16 c 0.92
a Since the alternative was "greater than" we find the p-value by the probability of being greater than the test statistic where we have 1.41 as the test statistic. Using the table we would subtract from one the proportion below 1.41 resulting in a p-value of 1 − 0.92 = 0.08
A hypothesis test was completed for an alternative hypothesis of Ha: μ < 40 resulting in a test statistic of − 1.17 From Table 8.1 what is the p-value for this test? a 0.12 b 0.24 c 0.88
a Since the alternative was less than we find the p-value by the probability of being less than the test statistic where we have 1.17 as the test statistic. Using the table we would find the p-value as the proportion below 1.17 which from the table is 0.12
A research team studied the effect of using technology on student outcomes. The study used statistical data from 20 different research studies representing a combined sample size of approximately 4,400 students. What statistical technique is being used? a Meta Analysis b Cluster Sampling c Stratified Sampling
a Since the study combined results across various prior studies this would be a meta analysis
A study is conducted to show that college women, on average, gain more weight than college men during their first year of college. The study is completed and reports a p-value of 0.001 What conclusion can be drawn? a The results are statistically significant; on average college women gain more weight than college men during their first year of college b The results are not statistically significant; there is not enough evidence to conclude that on average college women gain more weight than college men during their first year of college
a Since this p-value is less than 0.05 we would reject Ho and thus the results are statistically significant so there is enough evidence to conclude that on average college women gain more weight than college men during their first year of college
If a test of hypothesis using a two sided alternative produces a p-value of 0.002 then the p-value for a one sided alternative would simply be: a 0.001 b the same c 0.004
a The p-value for a one sided alternative is half the p-value from a two sided test. Thus the p-value would be 0.001
Which of the following is not one of the steps for hypothesis testing? a Assuming the alternative hypothesis is true, find the p-value. b Calculate a test statistic. c Assuming the null hypothesis is true, find the p-value. d Determine the null and alternative hypotheses.
a The p-value is found on the presumption that the null hypothesis is true, not the alternative.
Assume that two sample means are 15.0 and 10.0, and the corresponding SEMs are 3.0 and 4.0. What is an approximate 95% confidence interval for the difference in means? . a. 5 ± 2 x 5 b. 5 ± 2 x √7 c. 5 ± 2 x 25 d. 5 ± 2 x 7
a We find the SEM of the difference by taking the square root of the sum of the square of each individual SEM, 32 plus 42 equals 25 and the square root of 25 is 5. Then the 95% confidence interval for the difference would be equal to the difference in sample means, 5, ± 2 x 5
When a meta analysis is conducted and studies are combined, the combined result (i.e. the aggregated data result) may produce a result that conflicts with the results from the individual studies. This is an example of: a Simpson's Paradox b File drawer problem c Technology
a When studies are combined inappropriately result in the combined effect differing from the individual study effects is an example of Simpsons Paradox.
Which of the following intervals would you expect to be wider? a. 95% confidence interval b. 99% confidence interval c. 90% confidence interval
b The higher the level of confidence the wider the interval. This is true from a math perspective (i.e. as the level of confidence increases so does the multiplier used in that interval thus increasing the margin of error) and from common sense: the wider interval contains more possible outcomes and therefore you are more confident that the interval will contain the true value. For example, are you more confident that your next exam grade will be between 80 to 90 or 79 to 100?
Which of the following statements is true about a parameter and a statistic for samples taken from the same population? a. The value of the statistic varies from sample to sample. b. The value of the parameter varies from sample to sample.
a. The value of the statistic varies from sample to sample Only the value of the statistics will vary; the parameter is fixed
Say we calculated a 95% confidence interval for the mean number of nightly hours a PSU student sleeps during a week to between from 4.6 hours to 7.9 hours. Which of the following would represent the best interpretation of this interval? a. We are 95% confident that the true mean hours of sleep is between 4.6 and 7.9 hours. b. The 95% interval provides a narrower range of values than would a 90% confidence interval. c. There is a 95% probability that a randomly selected student sleeps between 4.6 and 7.9 hours.
a. We are 95% confident that the true mean hours of sleep is between 4.6 and 7.9 hours. Confidence intervals are exactly that: measures of how confident we are that our interval captures the true value.
Suppose that a polling organization surveys n = 400 people about whether they think the federal government should give financial aid to the airlines to help them avoid bankruptcy. In the poll, 300 people say that the government should provide aid to the airlines. Which choice gives the correct notation and value for the sample proportion, p-hat, in this survey? a. p-hat = 0.75 b. p = 0.30 c. p =0.75 d. p-hat = 0.30
a. p-hat= 0.75 The sample proportion, p-hat, would equal 300/400 = 0.75
When one considers all studies done on a particular topic and then counts the number of these studies that reported a statistically significant result is called: a Simpson's Paradox b Vote Counting Method c Combination Sampling d File Drawer Method
b
In hypothesis testing, a Type 1 error occurs when a the null hypothesis is rejected when the alternative hypothesis is true. b the null hypothesis is rejected when the null hypothesis is true. c the null hypothesis is not rejected when the null hypothesis is true. d the null hypothesis is not rejected when the alternative hypothesis is true.
b A Type 1 error happens when a null hypothesis that is actually true is incorrectly rejected.
Determine if the statement is a typical null hypothesis (Ho) or alternative hypothesis (Ha). The graduation rate for all division I athletes is not equal to the 85% claimed by the NCAA. a Null hypothesis b Alternative hypothesis
b Ho refers to no difference or change or equal to. Ha will be the research hypothesis that involves either a difference, greater than, or less than.
Which of the following is the correct definition of the power of a test of hypotheses? The probability to a Fail to reject the null hypothesis when in reality the null hypothesis is false b Reject the null hypothesis when in reality the null hypothesis is false c Reject the null hypothesis when reality the null hypothesis is true d Fail to reject the null hypothesis when in reality the null hypothesis is true
b Power is the probability of correctly rejecting the null hypothesis. That is, in reality the null hypothesis is false and your test decision is to reject Ho.
Which of the following is true about practical significance? Practical significance is a conclusion : a where everyone comes to the same conclusion after viewing the evidence b where a found statistical difference is also realistic or meaningful c that is based on the p-value of the test
b Practical significance implies that the results that are statistically significant are also useful, i.e. meaningful or realistic.
Since meta analysis can ONLY rely on those studies that have been previously published we can get a biased sample of studies. This is an example of the: a Simpson's Paradox b File drawer problem c Technology
b Since a meta analysis can only rely on those studies that have been published, there exists the possibility of most published studies reporting a significant finding. Therefore, going unreported and unpublished are those studies that did not have significant finding. These unreported studies are said to be left in the file drawer
A null hypothesis is that the mean nose lengths of men and women are the same. The alternative hypothesis is that men have a longer mean nose length than women. Which of the following is the correct way to state the null hypothesis? a Ho: p = 0.5 b Ho: μ1 − μ2 = 0 c Ho: p1 − p2 = 0
b Since nose lengths are quantitative the test would involve means. With men and women being compared this would involve two independent samples so the correct Ho would be Ho: μ1 − μ2 = 0
Is the given percent a statistic or a parameter? Of 200 students sampled from a class of stat 100, 160 or 80% said they would like the school library to have longer hours. a. Parameter b. Statistic
b Since the percent is from a sample it is a statistic.
Suppose that a difference between two groups is examined. In the language of statistics, the null hypothesis, Ho, is a statement that there is __________ a a difference between the groups for the populations. b no difference between the groups for the populations. c no difference between the groups for the samples. d a difference between the groups for the samples.
b The null hypothesis, Ho, would indicate that there is not a difference and that this would take place in the population. The sample is used to test for this population difference.
A counselor wants to show that for men who are married by the time they are 30, μ = average age when the men are married is not 21 years old. A random sample of 10 men who were married by age 30 showed an average age at marriage of 22.2, with a sample standard deviation of 1.9 years. Assume that the age at which this population of men gets married for the first time is normally distributed. What are the appropriate null and alternative hypotheses? a Ho: p = 21 and Ha: p > 21 b Ho: μ = 21 and Ha: μ ≠ 21 c Ho: p ≠ 21 and Ha: p = 21 d Ho: p = 21 and Ha: p < 21 e Ho: μ = 21 and Ha: μ >21 f Ho: μ ≠ 21 and Ha: μ = 21 g Ho: μ = 21 and Ha: μ h Ho: p = 21 and Ha: p ≠ 21
b The word not is the key term in determining the correct Ha expression and age is quantitative so this would be a means test. Not implies that the investigator is interested in whether the true population mean is not equal to 21. The symbol p is for proportion when the variable is categorical.
An investigator wants to assess whether the mean μ = the average weight of passengers flying on small planes exceeds the FAA guideline of average total weight of 185 pounds (passenger weight including shoes, clothes, and carry-on). Suppose that a random sample of 25 passengers showed an average total weight of 200 pounds. Assume that passenger total weights are normally distributed and the standard deviation is 50 pounds. What is the value of the test statistic? a test statistic = 7.5 b test statistic = 1.50 c test statistic = 0.3 d test statistic = negative 1.50
b This is a one sample t-test, so the test statistic, t is found by taking the difference between the sample mean (200) minus the hypothesized mean (185) and dividing by the standard error of the mean (S/√n = 50/√25 = 10). The t.s. = 15/10 = 1.50
Suppose we select a random sample of n = 100 students and find that the proportion of students who said they believe in love at first sight is 0.43. Which statement is not necessarily true? a. There were 43 students in the sample who said they believe in love at first sight. b. The population proportion p = 0.43 c. p-hat = 0.43 d. Based on the information provided by the sample, we cannot determine exactly what proportion of the population would say they believe in love at first sight.
b. The population proportion p = 0.43 p = 0.43 is a parameter representing the population proportion which would not necessarily be known just from the data given.
Which statement is correct about a p-value? a The smaller the p-value the stronger the evidence in favor the null hypothesis b Whether a small p-value provides evidence in favor of the alternative hypothesis depends on whether the test is one-sided or two-sided. c The smaller the p-value the stronger the evidence in favor of the alternative hypothesis. d Whether a small p-value provides evidence in favor of the null hypothesis depends on whether the test is one-sided or two-sided.
c A small p-value provides stronger evidence that the results produced by the sample did not occur by random chance but instead were the result of the null hypothesis being incorrect. Therefore, the smaller the p-value the stronger the evidence in support of the alternative hypothesis, Ha
Which of the following is NOT a potential problem with meta analysis? a File drawer problem b Simpson's Paradox c Increased sample size d Statistical versus practical significance
c Increased sample size is can be an advantage of a meta analysis and not so much a problem.
Statistic is to sample as parameter is to a. estimate. b. sample size. c. population. d. mean.
c Remeber: Statistic is to Sample as Population is to Parameter.
A hypothesis test was completed for an alternative hypothesis of Ha: μ ≠ 50 resulting in a test statistic of − 1.48 From Table 8.1 what is the p-value for this test? a 0.07 b 0.93 c 0.14
c Since the alternative was "not equal" we find the p-value by twice the probability of being greater than the absolute value of the test statistic where we have − 1.48 as the test statistic. Using the table we would subtract from one the proportion below 1.48 resulting in a p-value of 1 − 0.93 = 0.07 then double to get 0.14 as the final p-value.
Suppose that a difference between two groups is examined. In the language of statistics, the alternative hypothesis, Ha, is a statement that there is __________ a no difference between the groups for the populations. b no difference between the groups for the samples. c a difference between the groups for the populations. d a difference between the groups for the samples.
c The alternative hypothesis, Ha, would indicate that there is a difference and that this difference would take place in the population. The sample is used to test for this population difference.
suppose a 95% confidence interval for the proportion of Americans who exercise regularly is 0.29 to 0.37. Which one of the following statements is NOT true? a. An "acceptable" hypothesis is that about 33% of Americans exercise regularly. b. It is reasonable to say that more than 25% of Americans exercise regularly. c. It is reasonable to say that more than 40% of Americans exercise regularly. d. It is reasonable to say that fewer than 40% of Americans exercise regularly.
c The interval in the question has: an upper bound less than 40% making fewer than 40% true and thus more than 40%false. The lower bound being greater than 25% makes more than 25% acceptable and the interval range covers 33% making about 33% possible.
What is the primary purpose of a 95% confidence interval for a mean? a. to provide an interval that covers 95% of the individual values in the population b. to estimate a sample mean c. to estimate a population mean
c The primary purpose of a confidence interval is to estimate a population parameter.
Heights for a sample of n = 4 women are measured. For the sample, the mean is 64 inches and the standard deviation is 2 inches. Assuming that heights are normal/bell shaped, what is an approximate 95% confidence interval for the mean height of all women? a. 64 ± 2 x 0.5 b. 64 ± 2 x 2 c. 64 ± 2 x 1
c The standard error of the mean equals S/Sq.Rt. of n = 2/2 = 1 making an approximate 95% confidence interval equal to the sample mean 2 times SEM or 64 2 x 1
In a past General Social Survey, 87% of a random sample of n = 990 respondents answered yes to the question "Would you approve of an adult male punching a stranger if the stranger had broken into the man's house?" A 99% confidence interval for the proportion of all Americans who approve of punching an intruder is a. 0.87 ± 0.01 b. 0.87 ± 1.96 x 0.01 c. 0.87 ± 2.58 x 0.01 d. 0.87 ± 1.65 x 0.01
c. 0.87 ± 2.58 x 0.01 A confidence interval is found by sample statistic multiplier*StandardError. With p-hat of 0.87, multiplier of 2.58 and n = 990, the 99% confidence interval is 0.87 2.58 x 0.01
The cholesterol levels of a random sample of 100 men are measured. The sample mean is 188 and the standard deviation is 40. Which of the following provides an approximate 95% confidence interval for the population mean? a. 188 ± 2 x 0.4 b. 188 ± 2 x 40 c. 188 ± 2 x 4 d. 188 ± 2x 4000
c. 188 ± 2 x 4 The approximate 95% confidence interval is equal to the sample mean, 188, 2 times the SEM where the SEM (standard error of the mean) is equal to sd/n = 40/100 = 4
A null hypothesis is that the average pulse rate of adults is 70. For a sample of 64 adults, the average pulse rate is 71.8. A significance test is done and the p-value is 0.02. What is the most appropriate conclusion? a Reject the hypothesis that the sample average pulse rate is 70. b Conclude that the population average pulse rate is 70. c Conclude that the population average pulse rate is 71.8. d Reject the hypothesis that the population average pulse rate is 70.
d Since the p-value is less than 0.05 we would reject the Ho the null hypothesis that the population average pulse rate is 70.
A safety officer wants to prove that μ = the average speed of cars driven by a school is less than 25 mph. Suppose that a random sample of 16 cars shows an average speed of 24.0 mph. Assume that the speeds of cars are normally distributed with a standard deviation of 2 mph. What is the value of the test statistic? a test statistic = 0.5 b test statistic = 2.0 c test statistic = negative 0.5 d test statistic = negative 2.0
d This is a one sample t-test, so the test statistic is found by taking the difference between the sample mean (24) minus the hypothesized mean (25) and dividing by the standard error of the mean (S/n = 2/16 = 0.5). The t.s. = 1/0.5 = 2.0.
An investigator wants to assess whether the mean μ = the average weight of passengers flying on small planes exceeds the FAA guideline of average total weight of 185 pounds (passenger weight including shoes, clothes, and carry-on). Suppose that a random sample of 51 passengers showed an average total weight of 200 pounds with a sample standard deviation of 59.5 pounds. Assume that passenger total weights are normally distributed. What are the appropriate null and alternative hypotheses? a Ho: μ ≠ 200 and Ha: μ = 200 b Ho: μ ≠ 185 and Ha: μ = 185 c Ho: μ = 200 and Ha: μ ≠ 200 d Ho: μ =185 and Ha: μ < 185 e Ho: μ = 185 and Ha: μ > 185 f Ho: μ = 200 and Ha: μ > 200 g Ho: μ =200 and Ha: μ < 200 h Ho: μ = 185 and Ha: μ ≠ 185
e The word exceeds is the key term in determining the correct Ha expression. Exceeds implies that the investigator is only interested in whether the true population mean is greater than 185. The value of 200 is the sample mean.
