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

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

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...

Use the following information to answer the next 6 exercises.
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...

1. Assume that we want to construct a confidence interval. Do
one of the following, as appropriate: (a) find the critical value
t Subscript alpha divided by 2, (b) find the critical value z
Subscript alpha divided by 2, or (c) state that neither the
normal distribution nor the t distribution applies. Here are
summary statistics for randomly selected weights of newborn girls:
n=181, x= 33.7 hg, s= 7.6 hg. The confidence level is 99%.
a. tα/2e=
B. za/2 =...

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