Question

Question 202.5 pts

If we consider the simple random sampling process as an experiment, the sample mean is _____.

Group of answer choices

always zero

known in advance

a random variable

exactly equal to the population mean

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Question 212.5 pts

The basis for using a normal probability distribution to approximate the sampling distribution of x ¯ and p ¯ is called _____.

Group of answer choices

The Law of Repeated Sampling

The Central Limit Theorem

Expected Value

The Empirical Rule

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Question 222.5 pts

The sample mean ?̅ has a normal distribution _____.

Group of answer choices

if the sample size is greater than or equal to 30

if the sample size is less than 30

f the sample size is greater than or equal to 5

for any sample size

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Question 232.5 pts

The standard deviation of the distribution of the sample mean is called the _____.

Group of answer choices

standard error of the proportion

standard error of the mean

mean deviation

central variation

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Question 242.5 pts

The mean volume for a bottle of cologne is 4 ounces and the standard deviation is 0.22 ounces. A random sample of 121 bottles is taken. What is the standard error of the mean?

Group of answer choices

0.3636

0.0331

0.0200

4.000

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Question 252.5 pts

The mean volume for a bottle of cologne is 4 ounces and the standard deviation is 0.22 ounces. A random sample of 121 bottles is taken. What is the probability of obtaining a sample mean within 0.03 ounces of the population mean?

Group of answer choices

0.1074

0.5000

0.8664

0.9332

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Question 262.5 pts

What happens as the sample size increases?

Group of answer choices

The standard deviation of the population decreases.

The population mean increases.

The standard error of the mean decreases.

The standard error of the mean increases.

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Question 272.5 pts

As a general rule, the sampling distribution of the proportion can be approximated by a normal probability distribution whenever what condition(s) hold(s)?

Group of answer choices

np>5

n(1−p)>5

n>30

np>5andn(1−p)>5

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Question 282.5 pts

A study reports that only 12% of people stick to their New Year’s resolutions. Suppose you sample 100 people about whether they stuck to their resolutions. What is the standard error of the proportion?

Group of answer choices

0.0325

0.12

0.0001

10.6

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Question 292.5 pts

A study reports that only 12% of people stick to their New Year’s resolutions. Suppose you sample 100 people about whether they stuck to their resolutions. What is the probability that less than 8 out of 100 people respond that they did?

Group of answer choices

-1.23

0.1093

0.0400

0.2206

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Question 302.5 pts

A study reports that only 12% of people stick to their New Year’s resolutions. You are considering whether to sample 100 people or 200 people to verify the results of the study. With which sample size are you more likely to find a sample proportion that is close to the population proportion?

Group of answer choices

100

200

It doesn’t matter because a large sampling error is still possible with a large sample size.

It doesn’t matter because the probability of finding some range of sample means does not depend on sample size.

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Question 312.5 pts

The age (in years) of cars currently on the road in the U.S. is normally distributed. A researcher from the firm IHS Automotive selected a random sample of 30 cars and calculated the interval [10.39, 12.61] as the 90% confidence interval for the average age. The margin of error is _____.

Group of answer choices

2.22

1.64

1.11

1.82

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Question 322.5 pts

The weight of a package of Seattle’s Best ground coffee is normally distributed with a standard deviation of 0.7 ounces. A production manager at the company collects a random sample of 20 packages and finds a sample mean weight of 21.5 ounces. The 95% confidence interval for the average weight of a package of coffee is _____.

Group of answer choices

[20.0, 23.0]

[21.3, 21.7]

[22.9, 24.0]

[21.2, 21.8]

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Question 332.5 pts

Suppose you calculate a 90% confidence interval for the population mean and find the interval [2.8, 6.4]. The probability that the population means falls within this interval is _____.

Group of answer choices

0 or 1

90%

between 10% and 90%

at least 90%

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Question 342.5 pts

When the sample size increases, _____.

Group of answer choices

the margin of error and the standard error both decrease

the margin of error decreases and the standard error increases

the margin of error increases and the standard error decreases

the margin of error and the standard error both increase

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Question 352.5 pts

The systolic blood pressure was measured for a random sample of 25 adults. A 95% confidence interval for the population average systolic pressure ranged from 123 to 139. Which of the following is true?

Group of answer choices

If the sampling procedure would be repeated many times, 95% of the sample means would be between 123 and 139.

In the sample, 95% of adults had a systolic pressure between 123 and 139.

If the sampling procedure were repeated many times, 95% of the confidence intervals would contain the population average systolic pressure.

In the population, 95% of adults has a systolic pressure between 123 and 139.

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Question 362.5 pts

In a random sample of 16 observations from a normal distribution, ?̅ = 4.2. John calculates the sample standard deviation ? = 0.8 and uses this to construct a 90% confidence interval for the population mean. Sam, on the other hand, assumes that the population standard deviation ? = 0.8 and calculates a 90% confidence interval. Which of the following is true?

Group of answer choices

Sam’s margin of error is smaller than John’s.

Sam’s margin of error is larger than John’s.

Sam and John calculate the same margin of error.

There is not enough information to tell.

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Question 372.5 pts

As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution _____.

Group of answer choices

becomes smaller

becomes larger

stays the same

could become larger or smaller

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Question 382.5 pts

A random sample of 64 freshmen spent an average of 14 hours per week watching television. The sample standard deviation was 32 hours per week. What is the critical value for a 95% confidence interval for the population mean?

Group of answer choices

1.669

1.645

1.998

1.960

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Question 392.5 pts

A random sample of 64 freshmen spent an average of 14 hours per week watching television. The sample standard deviation was 32 hours per week. What is the 95% confidence interval for the population mean?

Group of answer choices

(6.01, 21.99)

(7.32, 20.68)

(6.16, 21.84)

(13.14, 14.86)

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Question 402.5 pts

In a random sample of 500 college students, 23% say they read or watch the news every day. What is the 90% confidence interval for the population proportion?

Group of answer choices

(0.217, 0.243)

(0.199, 0.261)

(0.206, 0.254)

(0.193, 0.267)

Answer 1

Solution:

20) If we consider the simple random sampling process as an experiment, the sample mean is a random variable. (in the question itself they have mentioned random sampling)

21)The basis for using a normal probability distribution to approximate the sampling distribution of x ¯ and p ¯ is called the Central Limit Theorem.

The central limit theorem (CLT) states that the distribution of sample means approximates a normal distribution as the sample size becomes larger, assuming that all samples are identical in size, and regardless of the population distribution shape.

22)The sample mean ?̅ has a normal distribution for any sample size.

If the population is normal to begin with then the sample mean also has a normal distribution, regardless of the sample size. For samples of any size drawn from a normally distributed population, the sample mean is normally distributed, with mean μˉX=μ and standard deviation σˉX=σ/√n, where n is the sample size.

23)The standard deviation of the distribution of the sample mean is called the standard error of the mean.

24)The mean volume for a bottle of cologne is 4 ounces and the standard deviation is 0.22 ounces. A random sample of 121 bottles is taken. What is the standard error of the mean?

Given: Mean=4 ounces, SD=0.22 ounces and n=121 bottles

Formula to calculate standard error is as follows:

S.E= SD/n=0.22/121=0.02

Option C is the correct answer.