Answered: According to a survey in a country,…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Question

100%

According to a survey in a country,

23%

of adults do not own a credit card. Suppose a simple random sample of

800

adults is obtained. Complete parts (a) through (d) below.

Click here to view the standard normal distribution table (page 1).

Click here to view the standard normal distribution table (page 2).

(a) Describe the sampling distribution of

the sample proportion of adults who do not own a credit card. Choose the phrase that best describes the shape of the sampling distribution of

below.

Not normal because

n≤0.05N

and np(1−p)≥10

Approximately normal because

n≤0.05N

and np(1−p)<10

Approximately normal because

n≤0.05N

and np(1−p)≥10

Not normal because

n≤0.05N

and np(1−p)<10

Determine the mean of the sampling distribution of

μp=nothing

(Round to two decimal places as needed.)

Determine the standard deviation of the sampling distribution of

σp=nothing

(Round to three decimal places as needed.)

(b) What is the probability that in a random sample of

800

adults, more than

24%

do not own a credit card?

The probability is

nothing.

(Round to four decimal places as needed.)

Interpret this probability.

If 100 different random samples of

800

adults were obtained, one would expect

nothing

to result in more than

24%

not owning a credit card.

(Round to the nearest integer as needed.)

800

adults, between

19%

and

24%

do not own a credit card?

The probability is

nothing.

(Round to four decimal places as needed.)

Interpret this probability.

If 100 different random samples of

800

adults were obtained, one would expect

nothing

to result in between

19%

and

24%

not owning a credit card.

(Round to the nearest integer as needed.)

(d) Would it be unusual for a random sample of

800

adults to result in

152

or fewer who do not own a credit card? Why? Select the correct choice below and fill in the answer box to complete your choice.

(Round to four decimal places as needed.)

The result

unusual because the probability that

is less than or equal to the sample proportion is

nothing,

which is

less

than 5%.

The result

is not

unusual because the probability that

is less than or equal to the sample proportion is

nothing,

which is

less

than 5%.

The result

is not

unusual because the probability that

is less than or equal to the sample proportion is

nothing,

which is

greater

than 5%.

The result

unusual because the probability that

is less than or equal to the sample proportion is

nothing,

which is

greater

than 5%.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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