Mean and Linear Regression - AP Statistics
Card 0 of 6
Suppose you conduct a paired 
-test to assess whether two group means significantly differ and find a 
-score of 1.645. At what alpha level would this cause you to reject the null?
Suppose you conduct a paired
The critical value for a 
-test with alpha set to 0.10 is 1.645.
The critical value for a
Compare your answer with the correct one above
Bob wants to statistically determine if the mean height of middle school boys is greater than the mean height of middle school girls. He wants to use a significance level of 
What must be true for him to reject 
. 
is known.
Bob wants to statistically determine if the mean height of middle school boys is greater than the mean height of middle school girls. He wants to use a significance level of
Step 1: We need to use a 2-sample z test because there are 2 samples, boys and girls. The population standard deviation, 
, is known, so we can assume a standard distribution for each sample.
Step 2: This is a one-sided z test because the questions asks if the mean height of boys is greater than the mean height of girls.
Step 3: significance level, or alpha, is 
. This means we need a p-value less than 
in order to reject the null hypothesis 
. A z-score greater than 
would ensure a p-value less than 
.
Step 1: We need to use a 2-sample z test because there are 2 samples, boys and girls. The population standard deviation,
Step 2: This is a one-sided z test because the questions asks if the mean height of boys is greater than the mean height of girls.
Step 3: significance level, or alpha, is
Compare your answer with the correct one above
No explanation available
No explanation available
Compare your answer with the correct one above
A statistician conducts a regression analysis and obtains a p-value of 0.1. It is more likely than not that there is a relationship between the variables in the study.
A statistician conducts a regression analysis and obtains a p-value of 0.1. It is more likely than not that there is a relationship between the variables in the study.
A p-value of 0.1 is generally not sufficient to reject the null hypothesis, but this is only because we want a high degree of confidence before finding a relationship between variables. Here, there is most likely a relationship between the variables even though the statistician could not reject the null hypothesis.
A p-value of 0.1 is generally not sufficient to reject the null hypothesis, but this is only because we want a high degree of confidence before finding a relationship between variables. Here, there is most likely a relationship between the variables even though the statistician could not reject the null hypothesis.
Compare your answer with the correct one above
Which of the following is an incorrect condition requirement for regression inference?
Which of the following is an incorrect condition requirement for regression inference?
All of the following choices are correct conditions except for the choice concerning a trend/pattern of some sort in the residual plot. For regression inference to be accurate, we need to look at the residual plot of the data of interest and make sure there is random scatter. Random scatter indicates that the ordered pairs are indeed independent of each other. Any sort of pattern present in the residual plot would not satisfy that requirement, and therefore would not enable us to successfully use regression inference.
All of the following choices are correct conditions except for the choice concerning a trend/pattern of some sort in the residual plot. For regression inference to be accurate, we need to look at the residual plot of the data of interest and make sure there is random scatter. Random scatter indicates that the ordered pairs are indeed independent of each other. Any sort of pattern present in the residual plot would not satisfy that requirement, and therefore would not enable us to successfully use regression inference.
Compare your answer with the correct one above
For a data set, the least-squares regression line has a 
confidence interval for the slope of 
.
Based on this confidence interval, what can you do with a hypothesis test at 
significance level where 
and 
?
For a data set, the least-squares regression line has a
Based on this confidence interval, what can you do with a hypothesis test at
Notice that the interval does not include 
. This means that the P-value for the hypothesis test would be under 5%, which would lead us to reject our null hypothesis.
Any confidence interval can be used to create a hypothesis test by inverting it, and it is fairly simple, but the concept is tested into graduate-level statistics theory.
Notice that the interval does not include
Any confidence interval can be used to create a hypothesis test by inverting it, and it is fairly simple, but the concept is tested into graduate-level statistics theory.
Compare your answer with the correct one above