Download CI Review Worksheet II

Name: __________________________________________
AP Statistics… z & t Intervals with Means Review
1) What is the critical value for a 96% confidence interval for a
sample of size 20? ( unknown)
a) 2.054
b) 1.96
c) 2.197
d) 2.205
e) 2.093
2) Which of the following statements is true?
a) A 95% confidence interval is narrower than a 90% confidence
interval for the same set of data.
b) Increasing the sample size will decrease the margin of error in
your confidence interval.
c) The critical value is the variance of the sampling distribution.
d) The point estimate is the measure of variation used in the
computation of the margin of error.
e) Smaller sample sizes produce larger margins of error because
smaller samples always have larger standard deviations.
3) Which of the following isn’t necessary to compute the sample size
appropriate for a given confidence level and margin of error?
a) x
b) 
c) z*
d) m (the margin of error)
e) All these values are necessary
4) You compute a 99% confidence interval with sample size A and a
margin of error of  5 units. You now wish to compute a 90%
confidence interval with the same margin of error with a sample
size B. For this situation, which of the following is true?
a)
b)
c)
d)
e)
B is greater than A
A is greater than B
A and B are equal
A must be twice as large as B
A equals the square root of B divided by the sample size
5) A sample of size 36 has s = 3 and yields the confidence interval
(23.5, 26.5). What is t*?
a) 0.5
b) 1
c) 3
d) 1.5
e) Not enough information to
answer
6) Which of the following is true?
I. In order to use t procedures, you must know the population
standard deviation.
II. t procedures are considered to be robust.
III. The standard error of the mean is an estimate of the
standard deviation of the sampling distribution of a sample
mean.
a) I only
b) II only
c) III only
d) I & II only
e) II and III only
7) El Burrito, a fast food chain, is attempting to standardize the
process in production of food items. It randomly selects 22
Grande Bean Burritos from stores around the country and weighs
them. The mean weight is 1.4 pounds and the standard deviation is
0.5 pounds. Assume that burrito weights are approximately
normally distributed. Which of the following is the correct
procedure to calculate a 96% confidence interval to estimate the
true mean weight of the Grande Bean Burritos?
 0.5 

 22 
 0.5 
1.4  2.054

 22 
 0.5 

1.4  2.189
 22 
a) 1.4  2.054
b)
c)
 0.5 

 22 
0.5 
e) 1.4  2.189

 22 
9) A researcher is interested in estimating the mean blood alcohol
content of people arrested for driving under the influence. Based
on past data, the researcher assumes a population standard
deviation of 0.065. What sample size is needed to estimate the
true mean blood alcohol content within .005 units at the 95%
confidence level?
a) 25
b) 26
c) 649
d) 1.4  2.183
10)
11)
a) Out of all the widgets produced in all widget factories, 90%
weigh between 7.2 and 8.9 pounds.
b) We can be 90% confident that all the widgets weigh between
7.2 and 8.9 pounds.
c) There’s a 90% chance the population mean is between 7.2 and
8.9 pounds.
d) Ninety percent of all sample means are equivalent to the true
mean weight of all widgets.
e) We are 90% confident that the true mean weight of widgets is
between 7.2 and 8.9 pounds.
Which of the following is a characteristic of the t distribution?
a)
b)
c)
d)
e)
8) A researcher computes a 90% confidence interval for the mean
weight (in pounds) of widgets produced at a factory. The interval
is (7.2, 8.9). Which of these is a correct interpretation of this
interval?
d) 650
e) Insufficient data to calculate
It contains a finite number of terms.
Its shape depends on the number of degrees of freedom.
It’s identical to the normal curve.
Its median is positive.
It can be used with a small sample size only if there are
outliers.
A group of dieters at a weight clinic are losing weight. Nine
patients have lost the following number of pounds in the past
month: 26.2, 17.2, 13.6, 13.4, 12.8, 11, 9.9, 6.2, and 7.9. Find
a 95% confidence interval for the mean weight loss for the
population of dieters at this clinic.
a) (9.28, 16.99)
b) (6.54, 19.73)
c) (8.60, 17.67)
d) (8.92, 17.53)
e) Normal assumption not met
12)
A teacher wants to estimate the mean difference between
grades in the fall and spring semesters of a specific course.
The fall semester averages were subtracted from the spring
semester averages for each student. A 95% confidence interval
is (-1.013, 6.069). Which of the following statements is true?
a) Since the confidence interval contains zero, we can say that
there is a significant mean difference between the grades in the
fall and spring semester.
b) Since the confidence interval contains zero, we cannot say that
there is a significant mean difference between the grades in the
fall and spring semester.
c) Since the confidence interval has more positive values, we can
say that there is a significant mean difference between the
grades in the fall and spring semester.
d) Since the confidence interval has some negative values, we can
say that there is a significant mean difference between the
grades in the fall and spring semester.
e) Since the confidence interval has some negative values, we
cannot say that there is a significant mean difference between
the grades in the fall and spring semester.
13)
Which of the following statements is false?
a) A 95% confidence interval is narrower than a 90% confidence
interval for the same data set.
b) The sample mean, x , is called a point estimate of the
population mean.
c) Increasing the sample size will decrease the margin of error in
your confidence interval.
d) As the sample size increases, the critical value t* approaches
the critical value z* for any given confidence level.
e) For a t distribution, the degree of freedom is n-1.