statistics
Dora likes to explore. Recently she explored Southeast Australia where she found some very large trees known as eucalyptus regnas or mountain ash. she wondered if they were taller on average than the coastal Douglas Firs of her native state of Oregon in the United States which have an average height of 250 ft in Old growth areas. Dora measured the heights of 15 mountain ash trees in southeast Australia and found an average height of these trees of 293 ft. Suppose s = 25 ft. Assume the heights of the 15 trees in Dora sample are representative of the heights of all mountain ash trees in southeast Australia. the T statistic for this problem is 6.661. How many degrees of freedom does this T statistic have?
14
the ___ is a value used in making a decision about the no hypothesis and is found by converting the sample statistic to a score with the assumption that the null hypothesis is true
WRONG: p value
a type 2 error is made...
a type 2 error is made when there is not enough evidence to reject the null hypothesis, but the null hypothesis is not true.
typically the direction (<,>, or ≠) used in the ___ hypothesis is determined from the question of Interest
alternative
a correlation coefficient close to 1 is evidence of a cause and effect relationship between the two variables
false
how is the best fitting line between the points in a scatter plot defined?
the line that gives the smallest sum of the squared vertical distances between each point and the line
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 50 college students and calculated a sample mean of 7.9 hours per night. The researcher performed a hypothesis test. What is the null hypothesis?
H0: ux = 8 hours per night
what notation is used for the null hypothesis?
H0
Clifford likes dogs. He wondered how much dog 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 local community and found that these 75 dog owners spend an average of $1,075 on their dogs in a year. Suppose population standard deviation = $175. Assume that these 75 dog owners are representative of all dog owners in terms of amount spent on their dogs in a year. State the alternative hypothesis
H1: ux > $1000
Dora likes to explore. Recently she explored Southeast Australia where she found some very large trees known as eucalyptus regnas or mountain ash. she wondered if they were taller on average than the coastal Douglas Firs of her native state of Oregon in the United States which have an average height of 250 ft in Old growth areas. Dora measured the heights of 15 mountain ash trees in southeast Australia and found an average height of these trees of 293 ft. Suppose s = 25 ft. Assume the heights of the 15 trees in Dora sample are representative of the heights of all mountain ash trees in southeast Australia. State the alternative hypothesis
HA: ux > 250
researchers wondered if brain size has an effect on a person's IQ. From a sample of 20 individuals, the equation of the least-squares regression line is y= 71.8 + 0.0286x, where X represents the size of a brain in cubic centimeters and Y represents IQ. What is the interpretation of the slope?
IQ is predicted to increase by 0.0286 for every one cubic centimeter increase in brain size
why is it important that the relationship between the explanatory and response variable B linear when performing a linear regression analysis?
WRONG: a non-linear relationship implies that the correlation coefficient is zero which implies no relationship exists between the explanatory and response variables
it is hypothesized that 50% of Americans attend church regularly. Which of the following would be an example of making a type 1 error?
WRONG: a study was conducted that had evidence to reject the null hypothesis. In reality, only 40% of Americans attend church regularly.
Steve calculated a correlation coefficient between gas price in miles driven as -0.15. Steve said there was a strong negative association between gas price and miles driven. Is this statement true or false?
WRONG: true
what is a variable other than X and Y that simultaneously affects both variables called?
a lurking variable
rejecting the null hypothesis when the null hypothesis is true is called ___
a type 1 error
is the nutritional information listed on food items accurate? Researchers randomly sampled 12 frozen dinners of a certain type from production during a particular period. the calorie content was determined. The stated calorie content on the package was 240 calories. Researchers wanted to determine if there was evidence to indicate that the mean calorie count was not equal to 240 calories using the one sample T methods. Which of the following statements is true?
the distribution of sample means will be normal only if the population data (that is, calorie content of all frozen dinners of this type produced during this particular period) follow a normal distribution
Clifford likes dogs. He wondered how much dog 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 local community and found that these 75 dog owners spend an average of $1,075 on their dogs in a year. Suppose population standard deviation = $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 is 0.0001. what conclusion should be made?
there is strong evidence that all dog owners spend more than $1,000 on their dogs each year on average
when is a t test performed instead of a z test
when the population standard deviation is not known
when performing a linear regression analysis, it is important that the relationship between the two quantitative variables be ___
linear
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 gpa's from a random sample of college students based on the normal probability plot, which of the following statements is correct?
WRONG: gpas of college students in this sample are approximately normally distributed. However because the sample is not representative of the population of all college students it cannot be said that the gpas of all college students follow a normal distribution.
a medical study was investigating whether getting a flu shot actually reduce the risk of developing the flu. A hypothesis test is to be performed. Which of the following statements is correct?
WRONG: a two tailed test will be performed since the alternative hypothesis states that the parameter is not equal to the hypothesized value
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. suppose the null hypothesis was rejected at 0.01. the power of the test was 0.80. What type of error could be made and what is the probability of making that error?
WRONG: a type 1 error could be made with the probability of 0.99
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 the data collected on gpa's from a random sample of college students. Based on the normal probability plot, which of the following statements is correct?
WRONG: gpas of college students in this sample are not approximately normally distributed. However because the sample is not representative of the population of all college students, it could be possible that the gpas of all college students follow a normal distribution.
data were collected on many different variables of a fast food chain sandwiches several years ago. two variables were the serving size in ounces of a sandwich and the number of calories in the sandwich. review the accompanying scatter plot of serving size versus number of calories. can the correlation coefficient be used to describe the strength of the relationship between serving size and number of calories?
WRONG: no because there are several extreme outliers that would have a strong influence on the correlation coefficient
the null and alternative hypotheses are determined ___ data are collected
before
the ___ hypothesis is a statement that the value of a population parameter is equal to some claimed value
null
a study was performed on teacher perceptions on the behavior of elementary school children. Teachers rated the aggressive behavior of a sample of 1450 New York City public school children by responding to the statement "this child threatens or bullies others in order to get his or her own way." Responses were measured on a scale ranging from 1 to 5. The summary statistics were sample mean = 2.15 and sample std. dev. = 1.05. Researchers wanted to test H0: ux = 3 versus HA: ux ≠3. Which of the following tests is the most appropriate to use (assuming all conditions for inference were satisfied)?
one sample T Test
Jan performed a study and obtained a p-value of 1.24. What conclusion should Jan make?
she made an error since it is not possible to get a P value of 1.24
describe the null and alternative hypotheses
the null hypothesis typically contains an equality while the alternative hypothesis will contain an inequality
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
Dora likes to explore. Recently she explored Southeast Australia where she found some very large trees known as eucalyptus regnas or mountain ash. she wondered if they were taller on average than the coastal Douglas Firs of her native state of Oregon in the United States which have an average height of 250 ft in Old growth areas. Dora measured the heights of 15 mountain ash trees in southeast Australia and found an average height of these trees of 293 ft. Suppose s = 25 ft. Assume the heights of the 15 trees in Dora sample are representative of the heights of all mountain ash trees in southeast Australia. Which hypothesis test should be used?
the one-sample T-Test
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?
the p-value must have been greater than 0.05
suppose increasing the sample size will not change the sample mean or the standard deviation. What will happen to the P value by increasing the sample size?
the p-value will decrease
which of the following Scatter Plots indicates a strong negative linear relationship between X and Y?
the plot with the points close together going gradually down
what does a correlation coefficient of 0 indicate?
there is no linear relationship between the two quantitative variables
data were collected on many different variables of a fast food chain sandwiches several years ago. two variables were the serving size in ounces of a sandwich and the number of calories in the sandwich. review the accompanying scatter plot of serving size versus number of calories. What is the correlation coefficient? try to figure out the correct answer without calculating the correlation coefficient.
+ 0.80
a p-value is the probability
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
Dora likes to explore. Recently she explored Southeast Australia where she found some very large trees known as eucalyptus regnas or mountain ash. she wondered if they were taller on average than the coastal Douglas Firs of her native state of Oregon in the United States which have an average height of 250 ft in Old growth areas. Dora measured the heights of 15 mountain ash trees in southeast Australia and found an average height of these trees of 293 ft. Suppose s = 25 ft. Assume the heights of the 15 trees in Dora sample are representative of the heights of all mountain ash trees in southeast Australia. State the null hypothesis
H0: the average height of all mountain ash trees in Southeast Asia is 250 ft, the same as the average height of typical old growth Douglas fir
Clifford likes dogs. He wondered how much dog 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 local community and found that these 75 dog owners spend an average of $1,075 on their dogs in a year. Suppose population standard deviation = $175. Assume that these 75 dog owners are representative of all dog owners in terms of amount spent on their dogs in a year. State the null hypothesis
H0: ux = $1000
Alex hypothesized that on average student study less than the recommended two hours per credit hour each week outside of class. Which of the following is the no hypothesis Alex will test?
H0: ux = 2 hours per week per credit
Alex hypothesized that on average student study less than the recommended two hours per credit hour each week outside of class. Which of the following is Alex's alternative hypothesis?
H1: u < 2 hours per week per credit
is the average body temperature of humans really 98.6 degrees Fahrenheit? After sampling 15600 healthy people from around the country, researchers found a sample mean of 98.5 degrees Fahrenheit. The p-value was 0.0001. Which of the following is true?
WRONG: the results are not statistically significant because the difference between the sample mean and the hypothesized value was not large
a medical study was investigating if getting a flu shot actually reduce the risk of developing the flu. From a group of adult volunteers, researchers randomly assigned half to receive an injection that contain the drug believed to reduce the risk of getting the flu and the other half to receive an injection containing no active ingredient. A hypothesis test was performed and a P value of 0.0002 was obtained. Which of the following statements is true?
WRONG: the small P value indicates strong evidence to reject the null hypothesis. Even though an experiment was performed causation cannot be inferred. That is, it cannot be concluded that the reduction in the risk of getting the flu was caused by the flu shot
Benjamin was investigating the relationship between outside temperature on a given day and number of hours spent outside that day. After sampling 25 people on 25 different days he obtained the displayed scatter plot. He should use the correlation coefficient to describe the strength of the relationship between temperature and hours spent outside.
WRONG: true
in a study conducted to examine the quality of fish after 7 Days in ice storage, 10 raw fish of the same kind and approximately the same size were caught and prepared for ice storage. The fish were placed and ice storage at different times after being caught. A measure of fish quality was given to each fish after 7 days in ice storage. Review the accompanying sample data, scatter plot, and minitab output from a simple linear regression analysis, where time is the number of hours after being caught the fish was placed in istorage and fish quality is the measure given to each fish after 7 days in ice storage. Is it appropriate to use this regression model to predict fish quality for fish put in storage 20 hours after it was caught?
WRONG: yes to predict fish quality determine the least-squares regression equation from the given output, substitute 20 into the equation for x and solve for y
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. What type of test should be performed?
a two tailed test should be performed since the alternative hypothesis states that the parameter is not equal to the hypothesized value
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 2 error?
from a study conducted, researchers failed to reject their null hypothesis. In fact 90% of Americans own cell phones
suppose the equation of a least squares regression line is y= -3.17 - 2.4x. What can be said about the y-intercept?
it is -3.17
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?
it is a one tailed test since the alternative hypothesis states that the parameter is greater than the hypothesized value
suppose the equation of a least squares regression line is y= -3.17 - 2.4x. What can be said about the correlation coefficient?
it is negative, but its exact value cannot be determined from the given information
data were collected on many different variables of a fast food chain sandwiches several years ago. two variables were the serving size in ounces of a sandwich and the number of calories in the sandwich. there are a couple of potential outliers-the sandwich with a serving size of around 6.75 Oz and about 260 calories, and the sandwich with a serving size of around 8.4 oz in about 720 calories. If these two observations were removed how would the correlation coefficient change?
it would increase since the removal of these data points makes the relationship stronger
are women getting taller? A researcher claims that the average height of a woman aged 20 years or older is greater than the 1994 mean height of 63.7 in. She obtains a random sample of 45 women aged 20 years or older and finds the sample mean to be 63.9 in. Assume the population standard deviation is 3.5 in. Which of the following tests is the most appropriate to use to test the researchers claim (assuming all conditions for inference are satisfied)?
one sample Z test
what is the definition of the correlation coefficient?
the correlation coefficient is a measure that describes the direction and strength of the linear relationship between two quantitative variables
Clifford likes dogs. He wondered how much dog 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 local community and found that these 75 dog owners spend an average of $1,075 on their dogs in a year. Suppose population standard deviation = $175. Assume that these 75 dog owners are representative of all dog owners in terms of amount spent on their dogs in a year. Which hypothesis test should be used?
the one sample Z test since the variable of interest is quantitative, there is one population, and the population standard deviation is known
there is a certain geyser that erupts on a regular basis. Researchers are interested in the relationship between the duration of a current eruption of the geyser and the time between when that eruption ends and the next eruption begins. Review the accompanying scatter plot of 222 eruptions of the geyser.
the point circled in red corresponds to an eruption that lasted about 3 minutes and had a time until the next eruption began of about 72 minutes after the eruption ended
when looking at a scatter plot of two quantitative variables, what do we typically look for?
the relationship between the two variables and if there are any deviations from the pattern (outliers or clusters of points for example)
there is a certain geyser that erupts on a regular basis. Researchers are interested in the relationship between the duration of a current direction of the geyser and the time between when that direction ends and the next eruption begins. Review the accompanying scatter plot of 222 eruptions of the guys are. The least-squares regression equation is y= 33.967 + 11.358x, where y is the interval from the end of the current option to the beginning of the next eruption and X is the duration of the current eruptions. In this equation what is 11.358?
the slope of the least-squares regression line
which of the following statements best describes this scatterplot?
there are two clusters of points. The relationship between X and Y for each cluster is strong and positive
Gina calculated a correlation coefficient between hours studied and grade point average as +0.75. which of the following is a correct statement based on this correlation coefficient?
there is a fairly strong positive relationship between hours studied and grade point average, indicating that grade point averages tend to be higher for students who study more
which of the following statements best describes this scatter plot?
there is a negative, moderately strong relationship between X and Y with one outlier
Clifford likes dogs. He wondered how much dog 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 local community and found that these 75 dog owners spend an average of $1,075 on their dogs in a year. Suppose population standard deviation = $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 is 0.0001. What conclusion should be made?
there is strong evidence to reject the null hypothesis
A p value is the probability that the null hypothesis is true
this statement is false. The null hypothesis will either be true or it won't be - there is no probability associated with this fact. 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
Alex calculated a correlation coefficient of -1.5. He made a mistake in his calculation since the correlation coefficient has to be between -1 and 1
true
Dora likes to explore. Recently she explored Southeast Australia where she found some very large trees known as eucalyptus regnas or mountain ash. she wondered if they were taller on average than the coastal Douglas Firs of her native state of Oregon in the United States which have an average height of 250 ft in Old growth areas. Dora measured the heights of 15 mountain ash trees in southeast Australia and found an average height of these trees of 293 ft. Suppose s = 25 ft. Assume the heights of the 15 trees in Dora sample are representative of the heights of all mountain ash trees in southeast Australia. the T statistic for this problem is 6.661. Based on this t-statistic which of the following is true?
with a p-value less than 0.0001, there is sufficient evidence to reject the null hypothesis and accept the alternative as true
