Exam 2
Based on a representative sample of college men, a regression line relating y = ideal weight to x = actual weight, for men, is given by: Ideal weight = 53 + 0.7x(actual weight) If a man weighs 200 pounds but his ideal weight is 210 pounds, then his residual is: -17 pounds 17 pounds -10 pounds 10 pounds
17 pounds
Which statement is not true about confidence intervals? A confidence interval is an interval of values computed from sample data that is likely to include the true population value. An approximate formula for a 95% confidence interval is sample estimate margin of error. A confidence interval between 20% and 40% means that the population proportion lies between 20% and 40%. A 99% confidence interval procedure has a higher probability of producing intervals that will include the population parameter than a 95% confidence interval procedure.
A confidence interval between 20% and 40% means that the population proportion lies between 20% and 40%.
Which one of the following choices describes a problem for which an analysis of variance would be appropriate? Comparing the proportion of successes for three different treatments of anxiety. Each treatment is tried on 100 patients. Comparing the mean birth weights of newborn babies for three different racial groups. Analyzing the relationship between high school GPA and college GPA. Analyzing the relationship between gender and opinion about capital punishment (favor or oppose).
Comparing the mean birth weights of newborn babies for three different racial groups.
An ESP experiment is done in which a participant guesses which of 4 cards the researcher has randomly picked, where each card is equally likely. This is repeated for 200 trials. The null hypothesis is that the subject is guessing, while the alternative is that the subject has ESP and can guess at higher than the chance rate. Which of the following would be a Type 1 error in this situation? Making a mistake in the calculations of the significance test. Declaring somebody does not have ESP when they actually do. Declaring somebody has ESP when they actually don't have ESP. Analyzing the data with a confidence interval rather than a significance test.
Declaring somebody has ESP when they actually don't have ESP.
Which choice is not an appropriate term for the x variable in a regression equation? Predictor variable Independent variable Dependent variable Explanatory variable
Dependent variable
A university administrator writes a report in which he states that at least 45% of all students have driven while under the influence of drugs or alcohol. Many others think the correct percent is less than 45%. What are the appropriate null and alternative hypotheses in this situation? H0: p = 0.45 vs. Ha: p≠≠ 0.45 H0: p ≥ 0.45 vs. Ha: p < 0.45 H0: p = 0.55 vs. Ha: p≠≠ 0.55 H0: p ≥ 0.55 vs. Ha: p < 0.55
H0: p ≥ 0.45 vs. Ha: p < 0.45
A regression equation is determined that describes the relationship between average January temperature (degrees Fahrenheit) and geographic latitude, based on a random sample of cities in the United States. The equation is: Temperature = 110 ‑ 2(Latitude) How does the estimated temperature change when latitude is increased by one? It goes down 2 degrees. It goes up 110 degrees. It goes up 2 degrees. It goes up 108 degrees.
It goes down 2 degrees.
It is known that for right-handed people, the dominant (right) hand tends to be stronger. For left-handed people who live in a world designed for right-handed people, the same may not be true. To test this, muscle strength was measured on the right and left hands of a random sample of 15 left-handed men and the difference (left - right) was found. The alternative hypothesis is one-sided (left hand stronger). The resulting t-statistic was 1.80. This is an example of: a paired t-test. an unpooled t-test. a two-sample t-test. a pooled t-test.
a paired t-test.
A statistically significant relationship between two categorical variables is illustrated in the sample as one that: is large enough that it is likely to have occurred in the observed sample even if there is no relationship in the population is small enough that it is likely to have occurred in the observed sample even if there is no relationship in the population. is small enough that it is unlikely to have occurred in the observed sample if there is no relationship in the population. is large enough that it is unlikely to have occurred in the observed sample if there is no relationship in the population
is large enough that it is unlikely to have occurred in the observed sample if there is no relationship in the population
Statistical inference takes information from the ___________ to the ____________. sample; population population; sample parameter; statistic interval; estimate
sample; population
A two-sided or two-tailed hypothesis test is one in which: the alternative hypothesis includes values in one direction from a specific standard the null hypothesis includes values in either direction from a specific standard. the null hypothesis includes values in one direction from a specific standard. the alternative hypothesis includes values in either direction from a specific standard
the alternative hypothesis includes values in either direction from a specific standard
The confidence level for a confidence interval for a mean is: the probability the procedure provides an interval that covers the sample mean. the probability of making a Type 1 error if the interval is used to test a null hypothesis about the population mean. the probability that individuals in the population have values that fall into the interval. the probability the procedure provides an interval that covers the population mean.
the probability the procedure provides an interval that covers the population mean.
What is the primary purpose of a 95% confidence interval for a mean? to estimate a sample mean to test a hypothesis about a sample mean to estimate a population mean to provide an interval that covers 95% of the individual values in the population
to estimate a population mean
One use of a regression line is: to determine if any y-values are outliers. to determine if any x-values are outliers. to estimate the change in y for a one-unit change in x. to determine if a change in x causes a change in y.
to estimate the change in y for a one-unit change in x.
A shopper wanted to test whether there was a difference in the average waiting times at the check-out counter among 5 different supermarkets. She selected a random sample of 20 shoppers from each of the five supermarkets. What is the alternative hypothesis for this situation? The average waiting time to check out is the same for all five supermarkets. The average waiting time to check out is 25 minutes for all five supermarkets. The average waiting time to check out is not the same for all five supermarkets. The average waiting time for each of the 100 shoppers is different.
The average waiting time to check out is not the same for all five supermarkets.
What is the main distinction between a confidence interval and a prediction interval? A prediction interval estimates the mean value of y at a particular value of x, while a confidence interval estimates the range of y values at a particular value of x. A confidence interval and a prediction interval are the same thing; they both estimate the mean value of y at a particular value of x. A confidence interval and a prediction interval are the same thing; they both estimate the range of y values at a particular value of x. A confidence interval estimates the mean value of y at a particular value of x, while a prediction interval estimates the range of y values at a particular value of x.
A confidence interval estimates the mean value of y at a particular value of x, while a prediction interval estimates the range of y values at a particular value of x.
A 95% confidence interval for the proportion of young adults who skip breakfast is found to be 0.20 to 0.27. Which of the following is the correct interpretation of the 95% confidence interval? There is a 95% probability that the proportion of young adults who skip breakfast is between 0.20 and 0.27. If this study were to be repeated with a sample of the same size, there is a 95% probability that the sample proportion would be between 0.20 and 0.27. We can be 95% confident that the sample proportion of young adults who skip breakfast is between 0.20 and 0.27. We can be 95% confident that the population proportion of young adults who skip breakfast is between 0.20 and 0.27.
We can be 95% confident that the population proportion of young adults who skip breakfast is between 0.20 and 0.27.
Suppose that a difference between two groups is examined. In the language of statistics, the alternative hypothesis is a statement that there is __________ no difference between the sample means. no difference between the population means. a difference between the sample means. a difference between the population means.
a difference between the population means.
The level of significance associated with a significance test is the probability: of not rejecting a true null hypothesis. that the null hypothesis is true. that the alternative hypothesis is true. of rejecting a true null hypothesis.
of rejecting a true null hypothesis.
The designated level (typically set at 0.05) to which the p-value is compared, in order to decide whether the alternative hypothesis is accepted or not is called a: statistically significant result. insignificant result. significance level. test statistic.
significance level.
Suppose that a 95% confidence interval for the proportion of first-year students at a school who played in intramural sports is 35% plus or minus 5%. The confidence level for the confidence interval is: 5% 35% 95% 100%
95%
Based on a representative sample of college men, a regression line relating y = ideal weight to x = actual weight, for men, is given by: Ideal weight = 53 + 0.7x(actual weight) For a man with actual weight = 200 pounds, his ideal weight is predicted to be: 253 pounds. 200 pounds. 193 pounds. 153 pounds.
193 pounds.
A regression equation is determined that describes the relationship between average January temperature (degrees Fahrenheit) and geographic latitude, based on a random sample of cities in the United States. The equation is: Temperature = 110 ‑ 2(Latitude) Estimate the average January temperature for a city at Latitude = 45. 30 degrees 20 degrees 10 degrees 45 degrees
20 degrees
A random sample of 100 students had a mean grade point average (GPA) of 3.2 with a standard deviation of 0.2. The standard error of the sample mean in this case is 0.02. Calculate an approximate 95% confidence interval for the mean GPA for all students. (2.8, 3.6) (3.16, 3.24) (3.18, 3.22) (3.00, 3.40)
(3.16, 3.24)
A university administrator writes a report in which he states that at least 45% of all students have driven while under the influence of drugs or alcohol. Many others think the correct percent is less than 45%. The z-statistic for this test is -2.41 and the p-value is 0.008. What conclusion should be made? There is insufficient evidence to conclude that the true proportion of students that has driven under the influence is less than 39%. Conclude that the true proportion of students that has driven under the influence appears to be less than 39%. Conclude that the true proportion of students that has driven under the influence appears to be less than 45%. There is insufficient evidence to conclude that the true proportion of students that has driven under the influence is less than 45%.
Conclude that the true proportion of students that has driven under the influence appears to be less than 45%.
Which of the following is a research question that could be addressed using a one-way analysis of variance? Does the variance of blood pressure differ for three different age groups? Are the proportions of people who oppose capital punishment different for three different age groups? Does mean blood pressure differ for three different age groups? Is there a relationship between political party preference and age?
Does mean blood pressure differ for three different age groups?
An ESP experiment is done in which a participant guesses which of 4 cards the researcher has randomly picked, where each card is equally likely. This is repeated for 200 trials. The null hypothesis is that the subject is guessing, while the alternative is that the subject has ESP and can guess at higher than the chance rate. What is the correct statement of the null hypothesis that the person does not have ESP? H0: p = 0.5 H0: p = 4/200 H0: p = 1/4 H0: p > 1/4
H0: p = 1/4
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? H0: μ =185 and Ha:μ≠ 185 H0: μ =185 and Ha:μ > 185 H0: μ =185 and Ha:μ < 185 H0: μ≠185 and Ha:μ = 185
H0: μ =185 and Ha:μ > 185
A chi-square test involves a set of counts called "expected counts." What are the expected counts? Hypothetical counts that would occur if the null hypothesis were true. Hypothetical counts that would occur if the alternative hypothesis were true. The actual counts that did occur in the observed data. The long-run counts that would be expected if the observed counts are representative.
Hypothetical counts that would occur if the null hypothesis were true.
A study was conducted to compare the mean sulfur dioxide concentrations for three cities. Independent random samples were obtained from each city and an ANOVA test was performed to compare the average sulfur dioxide concentrations among the three cities. The p-value for this F-test is 0.064. Suppose the necessary assumptions hold. Using a 5% significance level, which of the following is the correct conclusion? It appears that only one of the population mean concentration levels is significantly different from one of the others. It appears that the population mean concentration levels are all significantly different. It appears that at least one of the population mean concentration level is significantly different from at least one of the others. It appears that the mean concentration levels are approximately the same for the three city populations.
It appears that the mean concentration levels are approximately the same for the three city populations.
A shopper wanted to test whether there was a difference in the average waiting times at the check-out counter among 5 different supermarkets. She selected a random sample of 20 shoppers from each of the five supermarkets. What is the null hypothesis for this situation? The average waiting time to check out is the same for all five supermarkets. The average waiting time for each of the 100 shoppers is different. The average waiting time to check out is 25 minutes for all five supermarkets. The average waiting time to check out is not the same for all five supermarkets.
The average waiting time to check out is the same for all five supermarkets.
The r2 value is reported by a researcher to be 49%. Which of the following statements is correct? The explanatory variable explains 49% of the variability in the response variable. The response variable explains 70% of the variability in the explanatory variable. The response variable explains 49% of the variability in the explanatory variable. The explanatory variable explains 70% of the variability in the response variable.
The explanatory variable explains 49% of the variability in the response variable.
A study compared grade point averages (GPA) for students in a class: students were divided by 6 locations where they usually sat during lecture (i.e. left or right front, left or right center, left or right rear). A total sample size of 12 students was studied (2 students from each section) using one-way analysis of variance. The p-value for the F-test is 0.46. If the significance level = 0.05, what is the conclusion? The null hypothesis is not rejected so we can say the population means are different. The null hypothesis is rejected so we cannot say the population means are different. The null hypothesis is not rejected so we cannot say the population means are different. The null hypothesis is rejected so we can say the population means are different.
The null hypothesis is not rejected so we cannot say the population means are different.
A study compared testosterone levels among athletes in four sports: soccer, track, Lacrosse, and water polo. The total sample size was n =30 (10 soccer, 10 track, 5 Lacrosse, and 5 water polo). A one-way analysis of variance was used to compare the population mean levels for the four sports. The p-value for the F-test is = 0.02. Using the a = 0.05 significance level, what is the conclusion? The null hypothesis is not rejected: the means are significantly different. The null hypothesis is rejected: the means are not significantly different. The null hypothesis is not rejected: the means are not significantly different. The null hypothesis is rejected: the means are significantly different.
The null hypothesis is rejected: the means are significantly different.
Ninety people with high cholesterol are randomly divided into three groups of thirty, and a different treatment program for decreasing cholesterol is assigned to each group. The response variable is the change in cholesterol level after two months of treatment. An analysis of variance will be used to compare the three treatments. What null hypothesis is tested by this F-test? The sample means are equal for the three treatment groups. The sample variances are equal for the three treatment groups. The population means are equal for the three treatments The population variances are equal for the three treatments.
The population means are equal for the three treatments
The maximum distance at which a highway sign can be read is determined for a sample of young people and a sample of older people. The mean distance is computed for each age group. What's the appropriate null hypothesis about the means of the two groups? The population means are the same. The sample means are the same. The population means are different. The sample means are different.
The population means are the same.
An ESP experiment is done in which a participant guesses which of 4 cards the researcher has randomly picked, where each card is equally likely. This is repeated for 200 trials. The null hypothesis is that the subject is guessing, while the alternative is that the subject has ESP and can guess at higher than the chance rate. The subject actually gets 70 correct answers. Which of the following describes the probability represented by the p-value for this test? The probability of 70 or more correct guesses if the subject is guessing at the chance rate The probability that the subject is just guessing The probability of 70 or more correct guesses if the subject has ESP The probability that the subject has ESP
The probability of 70 or more correct guesses if the subject is guessing at the chance rate
About 90% of the general population is right-handed. A researcher speculates that artists are less likely to be right-handed than the general population. In a random sample of 100 artists, 83 are right-handed. Which of the following best describes the p-value for this situation? The probability that the population proportion of artists who are right-handed is 0.90 The probability that the population proportion of artists who are right-handed is 0.83 The probability the sample proportion would be as small as 0.83, or even smaller, if the population proportion of artists who are right-handed is actually 0.90 The probability that the population proportion of artists who are right-handed is less than 0.90, given that the sample proportion is 0.83
The probability the sample proportion would be as small as 0.83, or even smaller, if the population proportion of artists who are right-handed is actually 0.90
Which of the following relationships could be analyzed using a chi-square test? The relationship between height (inches) and weight (pounds). The relationship between opinion on gun control and income earned last year (in thousands of dollars). The relationship between satisfaction with K-12 schools (satisfied or not) and political party affiliation. The relationship between gender and amount willing to spend on a stereo system (in dollars).
The relationship between satisfaction with K-12 schools (satisfied or not) and political party affiliation.
An investigator wants to assess whether the mean m = 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. If the p-value for this test is 0.039, which of the following is an appropriate conclusion? The results are not statistically significant so there is not enough evidence to conclude the average total weight of all passengers is greater than 185 pounds. The results are statistically significant so the average total weight of all passengers appears to be less than 185 pounds. The results are statistically significant so the average total weight of all passengers appears to be greater than 185 pounds. The results are not statistically significant so there is not enough evidence to conclude the average total weight of all passengers is less than 185 pounds.
The results are statistically significant so the average total weight of all passengers appears to be greater than 185 pounds.
It is known that for right-handed people, the dominant (right) hand tends to be stronger. For left-handed people who live in a world designed for right-handed people, the same may not be true. To test this, muscle strength was measured on the right and left hands of a random sample of 15 left-handed men and the difference (left - right) was found. The alternative hypothesis is one-sided (left hand stronger). The resulting t-statistic was 1.80 and the p-value was less than 0.05. Which of the following is an appropriate conclusion? The results are statistically significant so the left hand appears to be stronger. The results are statistically significant so the left hand does not appear to be stronger. The results are statistically significant so the right hand appears to be stronger. The results are not statistically significant so there is not enough evidence to conclude the left hand appears to be stronger.
The results are statistically significant so the left hand appears to be stronger.
Which statement is correct about a p-value? Whether a small p-value provides evidence in favor of the alternative hypothesis depends on whether the test is one-sided or two-sided. Whether a small p-value provides evidence in favor of the null hypothesis depends on whether the test is one-sided or two-sided. The smaller the p-value the stronger the evidence in favor the null hypothesis The smaller the p-value the stronger the evidence in favor of the alternative hypothesis.
The smaller the p-value the stronger the evidence in favor of the alternative hypothesis.
The primary purpose of a significance test is to: decide whether there is enough evidence to support a research hypothesis about a sample. estimate the p-value of a sample. estimate the p-value of a population. decide whether there is enough evidence to support a research hypothesis about a population.
decide whether there is enough evidence to support a research hypothesis about a population.
A random sample of 600 adults is taken from a population of over one million, in order to compute a confidence interval for a proportion. If the researchers wanted to decrease the width of the confidence interval, they could: decrease the size of the population. decrease the size of the sample. increase the size of the population. increase the size of the sample.
increase the size of the sample.
The statistical significance of the association or relationship between two categorical variables is examined using a value known as the chi-square statistic, and a corresponding p-value that assesses the chance of getting this value for the Chi-square statistic or one even larger. Suppose the p-value of the test turns out to be 0.18. In this case, we should decide that: the observed relationship most likely did not occur by chance, so we can say that the relationship is statistically significant. the observed relationship could have occurred by chance, so we cannot say that the relationship is statistically significant there is only an 18% chance that the observed relationship occurred by chance, so we can say that the relationship is statistically significant. the observed relationship most likely did not occur by chance, so we cannot say that the relationship is statistically significant.
the observed relationship could have occurred by chance, so we cannot say that the relationship is statistically significant
A regression line is used for all of the following except one. Which one is not a valid use of a regression line? to estimate the change in y for a one-unit change in x. to estimate the average value of y at a specified value of x. to predict the value of y for an individual, given that individual's x-value. to determine if a change in x causes a change in y.
to determine if a change in x causes a change in y.
What is the primary purpose of doing a chi-square test? to estimate a population proportion to determine if there is a significant relationship between two quantitative variables to determine if there is a significant relationship between two continuous variables to determine if there is a significant relationship between two categorical variables
to determine if there is a significant relationship between two categorical variables
Which expression is a regression equation for a simple linear relationship in a sample? E ( Y ) = β0 + β1 E ( Y ) = β0 + β 1x + β2 x^2 y(hat)= b0 + b1 x y(hat)= 44 + 0.60 x1 + .45 x2
y(hat)= b0 + b1 x