Deck 13: Sampling Distribution Models and Confidence Intervals for Proportions

Question 1

Assume that 15% of students at a university wear contact lenses.We randomly pick 200 students.What is the mean of the proportion of students in this group who may wear contact lenses?

A) $\mu = 5.48 \%$
B) $\mu = 2.52 \%$
C) $\mu = 7.5 \%$
D) $\mu = 15 \%$
E) $\mu = 30 \%$

Answer 1

$\mu = 15 \%$

Question 2

A survey found that 79% of a random sample of 1024 American adults approved of cloning endangered animals.Find the margin of error for this survey if we want 90% confidence in our estimate of the percent of American adults who approve of cloning endangered animals.

A)2.49%
B)21.4%
C)2.09%
D)5.43%
E)4.56%

Answer 2

2.09%

Question 3

In a large class, the professor has each person toss a coin several times and calculate the proportion of his or her tosses that were heads.The students then report their results, and the professor plots a histogram of these several proportions.If the students toss the coin 100 times each, about 68% should have proportions between what two numbers?
Use the 68-95-99.7 Rule to provide the appropriate response.

A)0.34 and 0.67
B)0.45 and 0.55
C)0.16 and 0.84
D)0.495 and 0.505
E)0.05 and 0.1

Answer 3

0.45 and 0.55

Question 4

A survey of shoppers is planned to see what percentage use credit cards.Prior surveys Suggest 54% of shoppers use credit cards.How many randomly selected shoppers must we Survey in order to estimate the proportion of shoppers who use credit cards to within 1% with 95% confidence?

A)16,471
B)8589
C)20,745
D)6718.3
E)9543

Question 5

Based on past experience, a bank believes that 7% of the people who receive loans will not make payments on time.The bank has recently approved 300 loans.What is the probability that over 8% of these clients will not make timely payments?

A)0.752
B)0.504
C)0.248
D)0.68
E)0.496

Question 6

When 346 college students are randomly selected and surveyed, it is found that 121 own a car. Construct a 99% confidence interval for the percentage of all college students who own a car.

A)(12.1%, 57.8%)
B)(29.9%, 40.0%)
C)(29.0%, 40.9%)
D)(28.4%, 41.6%)
E)(30.8%, 39.2%)

Question 7

After conducting a survey, a researcher wishes to cut the standard error (and thus the marginof error) to of its original value.How will the necessary sample size change?

A)It will decrease by a factor of 3.
B)It will increase by a factor of 3.
C)It will decrease by a factor of 9.
D)It will increase by a factor of 9.
E)Not enough information is given.

Question 8

Based on past experience, a bank believes that 6% of the people who receive loans will not make payments on time.The bank has recently approved 300 loans.What is the standard deviation of the proportion of clients in this group who may not make timely payments?

A) $\sigma = 1.88 \%$
B) $\sigma = 1.41 \%$
C) $\sigma = 1.37 \%$
D) $\sigma = 4.11 \%$
E) $\sigma = 4.24 \%$

Question 9

In a survey of 300 T.V.viewers, 40% said they watch network news programs.Find the margin of error for this survey if we want 95% confidence in our estimate of the percent of T.V.viewers who watch network news programs.

A)4.16%
B)7.28%
C)6.37%
D)5.54%
E)8.36%

Question 10

In a poll of 929 voters in a certain city, 68% said that they backed a bill which would limit Growth and development in their city.The margin of error in the poll was reported as 3 Percentage points (with a 95% degree of confidence).Which statement is correct?

A)The reported margin of error is consistent with the sample size.
B)The sample size is too large to achieve the stated margin of error.
C)For the given sample size, the margin of error should be smaller than stated
D)The sample size is too small to achieve the stated margin of error.

Question 11

Assume that 15% of students at a university wear contact lenses.We randomly pick 200 students.What is the probability that more than 16% of this sample wear contact lenses?

A)0.309
B)0.397
C)0.654
D)0.346
E)0.692

Question 12

In a poll of 268 voters in a certain city, 60% said that they backed a bill which would limit growth and development in their city.The margin of error in the poll was reported as 6 percentage points (with a 95% degree of confidence).Which statement is correct?

A)The stated margin of error could be achieved with a larger sample size.
B)The reported margin of error is consistent with the sample size.
C)The stated margin of error could be achieved with a smaller sample size.
D)The sample size is too small to achieve the stated margin of error.
E)There is not enough information to determine whether the margin of error is consistent with the sample size.

Question 13

In a large class, the professor has each person toss a coin several times and calculate the proportion of his or her tosses that were heads.The students then report their results, and the professor plots a histogram of these several proportions.If the students toss the coin 80 times each, about 95% should have proportions between what two numbers?
Use the 68-95-99.7 Rule to provide the appropriate response.

A)0.025 and 0.975
B)0.39 and 0.62
C)0.1118 and 0.1677
D)0.4875 and 0.5125
E)0.2375 and 0.7375

Question 14

The number of hours per week that high school seniors spend on homework is normally distributed, with a mean of 10 hours and a standard deviation of 3 hours.60 students are chosen at random.Let represent the mean number of hours spent on homework for this group.Find the probability that is between 9.8 and 10.4.

A)0.547
B)0.5161
C)0.080
D)0.1528
E)0.3043

Question 15

Assume that 10% of students at a university wear contact lenses.We randomly pick 200 students.What is the standard deviation of the proportion of students in this group who may wear contact lenses?

A) $\sigma = 4.5 \%$
B) $\sigma = 2.24 \%$
C) $\sigma = 2.12 \%$
D) $\sigma = 4.47 \%$
E) $\sigma = 4.24 \%$

Question 16

A university's administrator proposes to do an analysis of the proportion of graduates who have not found employment in their major field one year after graduation.In previous years, the percentage averaged 15%.He wants the margin of error to be within 5% at a 99% confidence level.What sample size will suffice?

A)17
B)138.3
C)407
D)196
E) 339

Question 17

Of 346 items tested, 12 are found to be defective.Construct a 98% confidence interval for the Percentage of all such items that are defective.

A)(0.13%, 6.80%)
B)(3.34%, 3.59%)
C)(0.93%, 6.00%)
D)(1.85%, 5.09%)
E)(1.18%, 5.76%)

Question 18

Based on past experience, a bank believes that 4% of the people who receive loans will not make payments on time.The bank has recently approved 300 loans.What is the mean of the proportion of clients in this group who may not make timely payments?

A) $\mu = 4 \%$
B) $\mu = 3.46 \%$
C) $\mu = 1.1 \%$
D) $\mu = 2 \%$
E) $\mu = 12 \%$

Question 19

Question 20

The number of hours per week that high school seniors spend on computers is normally distributed, with a mean of 4 hours and a standard deviation of 2 hours.60 students are chosen at random.Let represent the mean number of hours spent on the computer for this group.Find the probability that is between 4.2 and 4.4.

A)0.041
B)0.159
C)0.317
D)0.720
E)0.775