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AP Stats Confidence Intervals for Means

Total questions: 22

Worksheet time: 1hrs 3mins

Name
Class
Date
1.

2000 children were surveyed and the report that followed said, "With 98% confidence, between 20% and 50% of all parents make their children eat breakfast." What does 98% confidence mean in this situation?

a)

We can be 98% confident that the method used to get the intervals always gives the correct answer

b)

98% of all parents will make their kids eat breakfast

c)

When used repeatedly, the method used to find the interval produces intervals which include the true proportion about 98% of the time

d)

The kids were 98% confident that they ate breakfast that day.

2.

Mrs. Soto polled 1000 adults and estimated with 90% confidence that the proportion of adults who have dessert after dinner is .75. Ms. Libner thinks that 90% confidence isn't enough and wants to do a 95% confidence. How would a margin of error for 95% compare with a ME for 90% if the same sample size was used?

a)

It would be smaller because a higher confidence means a smaller MOE

b)

It would be larger because a higher confidence means a larger MOE

c)

It would be the same because the sample size is the same

d)

Won't be able to tell without knowing the true parameter

3.

The heights of 5-year old boys are approximately normal. The mean height of a random sample of 37 5-year old boys is found to be 30 inches with a standard deviation of 3 inches. What is the standard error of x̄?

a)

.493

b)

1.32

c)

5.77

d)

1.96

4.

A survey of a random sample of 2500 adults who have a credit card found that 570 had a balance of $1000 or more on their credit card.

What would NOT be a condition we need to verify before constructing the interval?

a)

np̂ ≥ 10 and n(1-p̂) ≥ 10

b)

n ≥ 30

c)

10% condition

d)

random sample

5.

A survey of a random sample of 2500 adults who have a credit card found that 570 had a balance of $1000 or more on their credit card.

What symbol would you use to describe the parameter?

a)

μ

b)

p

c)

d)

6.

Which of the following would not decrease the width of a confidence interval?

I. Increasing the sample size

II. Decreasing the degrees of freedom

III. Decreasing the confidence level

a)

I only

b)

II only

c)

III only

d)

I and II only

e)

II and III only

7.
An irate patient complained that the cost of a doctor's visit was too high.  She randomly surveyed 20 other patients and found that the mean amount of money they spent on each doctor's visit was $44.80.  The standard deviation of the sample was $3.53.  Find the 95% confidence interval of the population mean.
a)
$43.15 - $46.45
b)
$44.53 - $48.21
c)
$42.65 - $48.25
d)
$43.15 - $48.25
8.
In a study of 150 accidents that required treatment in an emergency room, 36% involved children under 6 years of age.  Find the 90% confidence interval of the true proportion of accidents that involve children under the age of 6.
a)
0.331 - 0.413
b)
0.275 - 0.433
c)
0.295 - 0.425
d)
0.255 - 0.455
9.
At a particular college, 78% of all students are receiving some kind of financial aid.The school newspaper selects a random sample of 100 students and 72% of the respondents say they are receiving some sort of financial aid. Which of the following is true?
a)
 78% is a population and 72% is a sample.
b)
72% is a population and 78% is a sample
c)
78% is a parameter and 72% is a statistic
d)
72% is a parameter and 78% is a statistic
10.
What does this symbol represent?
a)
population proportion
b)
parameter
c)
sample proportion
d)
population sample
11.
Agricultural researchers plant 100 plots with a new variety of corn and measure the mean yield for these plots in bushels per acre. They treat the 100 plots as a simple random sample of possible plots of corn (as researchers often do) and report a 95% confidence interval for the mean corn yield of (128.4, 131.6) bushels per acre. Which of the following is a correct interpretation of the 95% confidence level?
a)
We are 95% confident that the true mean yield for this new variety of corn is captured by the interval (128.4, 131.6) bushels per acre
b)
If many intervals were constructed this way from many independent sets of 100 plots, 95% of the intervals would capture the true mean corn yield.
c)
If many intervals were constructed this way from many independent sets of 100 plots, 95% of the time the true mean corn yield would be in the interval (128.4, 131.6) bushels per acre.
12.
A 90% confidence interval for the average salary of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. The interval was ($139,048, $154,144). Give a practical interpretation of the interval.
a)
90% of the sampled CEOs have salaries that fell in the interval $139,048 to $154,144
b)
We are 90% confident that the mean salary of all CEOs in the electronics industry falls in the interval $139,048 to $154,144. 
c)
90% of all CEOs in the electronics industry have salaries that fall between $139,048 to $154,144
d)
We are 90% confident that the mean salary of the sampled CEOs falls in the interval $139,048 to $154,144.
13.
The 90% interval for a statistics test was given by 72 +- 7. What is the lower bound for the interval?
a)
7
b)
72
c)
65
d)
79
14.

A study found that in a sample of 44 subjects, 9 of them agree that children under 6 shouldn’t be taken to nice restaurants.


The 95% confidence interval for p is (0.082, 0.318). Interpret this interval.

a)

95% of the time the proportion of people who believe children under 6 shouldn't be taken to nice restaurants will be between 8.2% and 31.8%.

b)

The population proportion of people who believe children under 6 shouldn't be taken to nice restaurants is between 8.2% and 31.8%.

c)

The probability that the proportion of people who believe children under 6 shouldn't be taken to nice restaurants will be between 8.2% and 31.8% is 95%.

d)

Based on this sample, I am 95% confident that the proportion of people who believe children under 6 shouldn't be taken to nice restaurants is between 8.2% and 31.8%.

15.
Which z-value is used for a 95% confidence interval?
a)
1.65
b)
1.96
c)
2.58
d)
2.33
16.
Which of the following changes to a study would result in a narrower confidence interval?
a)
increasing the confidence level, increasing the sample size
b)
decreasing the confidence level, decreasing the sample size
c)
increasing the confidence level, decreasing the sample size
d)
decreasing the confidence level, increasing the sample size.
17.

Mr. Reinecke wants to estimate the proportion of seniors who will go to college next year with 96% confidence and a margin of error of no more than 5%. What size sample does he need to take?

a)

422

b)

419

c)

410

d)

400

18.

Mrs. Soto polled 1000 adults and estimated with 90% confidence that the proportion of adults who have dessert after dinner is .75. Ms. Libner thinks that 90% confidence isn't enough and wants to do a 95% confidence. How would a margin of error for 95% compare with a ME for 90% if the same sample size was used?

a)

It would be smaller because a higher confidence means a smaller MOE

b)

It would be larger because a higher confidence means a larger MOE

c)

It would be the same because the sample size is the same

d)

Won't be able to tell without knowing the true parameter

19.

You want to calculate a 98% confidence interval for a population mean with a sample of n = 20. What is the appropriate t*?

a)

2.326

b)

2.528

c)

2.539

d)

2.518

20.

Mrs. Soto wants to find the sample size needed to find with 95% confidence the mean amount of time her stats students spent on homework during the snow days. The population is approximately normal and the known standard deviation is 6 minutes. How large should the sample size be if she wants a margin of error of +- .5 minutes?

a)

553

b)

551

c)

600

d)

601

21.

A survey of a random sample of 2500 adults who have a credit card found that 570 had a balance of $1000 or more on their credit card.

What would be the margin of error if you had a 99% confidence?

a)

0.022

b)

0.0046

c)

0.008

d)

0.016

22.

A researcher wants to find a confidence interval estimate of the mean time it takes to complete an order over the phone at a call center for a large retail company. He has selected a random sample of 18 orders and recorded the time to complete the order. The sample mean time was 4.27 minutes and the sample standard deviation was 0.78 minutes. Assuming the conditions needed for inference are met, which of the following is the appropriate 98% confidence interval?

a)

4.27 ± 2.326 ⋅ (0.78/√18)

b)

4.27 ± 2.054 ⋅ (0.78/√18)

c)

4.27 ± 2.552 ⋅ (0.78/√18)

d)

4.27 ± 2.567 ⋅ (0.78/√18)

e)

4.27 ± 2.567 ⋅ (0.78/√17)