Question

True or false? A larger sample size produces a longer confidence interval for μ.

False. As the sample size increases, the maximal error decreases, resulting in a shorter confidence interval.True. As the sample size increases, the maximal error decreases, resulting in a longer confidence interval.    True. As the sample size increases, the maximal error increases, resulting in a longer confidence interval.False. As the sample size increases, the maximal error increases, resulting in a shorter confidence interval.

True or false? If the sample mean x of a random sample from an x distribution is relatively small, when the confidence level c is reduced, the confidence interval for μ becomes shorter.

True. As the level of confidence decreases, the maximal error of estimate increases.False. As the level of confidence decreases, the maximal error of estimate decreases.    False. As the level of confidence decreases, the maximal error of estimate increases.True. As the level of confidence decreases, the maximal error of estimate decreases.

As the degrees of freedom increase, what distribution does the Student's t distribution become more like?

uniform standard normal    binomial chi-square

Lorraine was in a hurry when she computed a confidence interval for μ. Because σ was not known, she used a Student's t distribution. However, she accidentally used degrees of freedom n instead of n − 1. Will her confidence interval be longer or shorter than one found using the correct degrees of freedom n − 1? Explain.

Shorter. As the degrees of freedom increase, the value for t_c increases.Longer. As the degrees of freedom increase, the value for t_c increases.    Longer. As the degrees of freedom increase, the value for t_c decreases.Shorter. As the degrees of freedom increase, the value for t_c decreases.

Which combination of factors would definitely reduce the width of a confidence interval?

use a smaller sample and increase the level of confidenceuse a smaller sample and decrease the level of confidence    use a larger sample and increase the level of confidenceuse a larger sample and decrease the level of confidence

The standard deviation of the weights of elephants is known to be approximately 15 pounds. We wish to construct a 95% confidence interval for the mean weight of newborn elephant calves. Fifty newborn elephants are weighed. The sample mean is 244 pounds. The sample standard deviation is 11 pounds.

In words, define the random variables X and X.

X is the weight in pounds of a newborn elephant, and X is the average of weights of the sample of 50 baby elephants.X is the weight in pounds of a newborn elephant, and X is the sample mean of the 50 baby elephants.    X is the weight in pounds of a newborn elephant, and X is the standard deviation of the weights of baby elephants.X is the sample mean of the weights of the sample of 50 newborn elephant, and X is the sample standard deviation of weights of the sample of 50 baby elephants.X is the average of weights of the sample of 50 newborn elephant, and X is the weight in pounds of a baby elephant.

A sample of 20 heads of lettuce was selected. Assume that the population distribution of head weight is normal. The weight of each head of lettuce was then recorded. The mean weight was 2.2 pounds with a standard deviation of 0.1 pounds. The population standard deviation is known to be 0.2 pounds.

In complete sentences, give an interpretation of what the 95% confidence interval for the population mean weight of the heads of lettuce means.

We are 95% confident that the weight of a head of lettuce lies within this interval.We are 95% confident that the true population mean weight of all weights of heads of lettuce lies within this interval.    There is a 95% chance that the weight of a head of lettuce lies within this interval.We are 95% confident that the mean weight of the sample of 20 heads of lettuce lies within this interval.

The Ice Chalet offers dozens of different beginning ice-skating classes. All of the class names are put into a bucket. The 5 P.M., Monday night, ages 8 to 12, beginning ice-skating class was picked. In that class were 64 girls and 16 boys. Suppose that we are interested in the true proportion of girls, ages 8 to 12, in all beginning ice-skating classes at the Ice Chalet. Assume that the children in the selected class are a random sample of the population.

In words, define the random variable X.

the time of the beginning ice-skating classthe total number of children in beginning ice-skating classes    the number of girls, ages 8 to 12, in the beginning ice-skating classthe number of boys, ages 8 to 12, in the beginning ice-skating classthe number of beginning ice-skating classes

The Ice Chalet offers dozens of different beginning ice-skating classes. All of the class names are put into a bucket. The 5 P.M., Monday night, ages 8 to 12, beginning ice-skating class was picked. In that class were 64 girls and 16 boys. Suppose that we are interested in the true proportion of girls, ages 8 to 12, in all beginning ice-skating classes at the Ice Chalet. Assume that the children in the selected class are a random sample of the population.

In words, define the random variable .

the number of girls, ages 8 to 12, in the beginning ice-skating classthe number of children in the beginning ice-skating class    the proportion of girls, ages 8 to 12, in the beginning ice-skating classthe number of boys, ages 8 to 12, in the beginning ice-skating classthe proportion of boys, ages 8 to 12, in the beginning ice-skating class

True or false? Every random sample of the same size from a given population will produce exactly the same confidence interval for μ.

False. Different random samples may produce different x values, resulting in different confidence intervals.True. Different random samples will produce the same x values, resulting in the same confidence intervals.    False. Different random samples may produce different x values, resulting in the same confidence intervals.True. Different random samples may produce different x values, resulting in different confidence intervals.

Answer 1

Que.1

Marginal error =

As n increases, standard error decreases. Hence we get shorter confidence interval.

False. As the sample size increases, the maximal error decreases, resulting in a shorter confidence interval.

Que.2

True. As the level of confidence decreases, the maximal error of estimate decreases.

Que.3

As the degrees of freedom increase, the Student's t distribution become more likely to standard normal.

Que.4

Shorter. As the degrees of freedom increase, the value for tc decreases

Que.5

use a larger sample and decrease the level of confidence, this combination of factors would definitely reduce the width of a confidence interval