Mean and Linear Regression - AP Statistics

The critical value for a -test with alpha set to 0.10 is 1.645.

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 .

No explanation available

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.

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.

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.

The critical value for a -test with alpha set to 0.10 is 1.645.

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 .

No explanation available

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.

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.

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.

The critical value for a -test with alpha set to 0.10 is 1.645.

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 .

No explanation available

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.

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.

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.

The critical value for a -test with alpha set to 0.10 is 1.645.

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 .