# The population proportion and sample proportion always have the same value.

1. The population proportion and sample proportion always has
the same value.
True or false?

A. True

B. False

A. True

B. False

A. True

A. True

B. False

B. False

Question 2 of 13
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Question 2 of 13
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Question 2 of 13
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Question 2 of 13 1.0 Points Without doing any computation, decide which has a higher
probability, assuming each sample is from a population that is
normally distributed with a mean equal to 100 and a standard
deviation equal to 15. Explain your reasoning.
(a) P(90?sample mean?110) for a random sample of size n = 10
(b) P(90?sample mean?110) for a random sample of size n = 20

A. P(90?sample mean?110) for a random sample of size n = 20 has
a higher probability. As n increases, the standard deviation
decreases.

B. P(90?sample mean?110) for a random sample of size n = 10 has
a higher probability. As n increases, the standard deviation
increases.

C. P(90?sample mean?110) for a random sample of size n = 10 has
a higher probability. As n increases, the standard deviation
decreases.

D. P(90?sample mean?110) for a random sample of size n = 20 has
a higher probability. As n increases, the standard deviation
increases.

A. P(90?sample mean?110) for a random sample of size n = 20 has
a higher probability. As n increases, the standard deviation
decreases.

B. P(90?sample mean?110) for a random sample of size n = 10 has
a higher probability. As n increases, the standard deviation
increases.

C. P(90?sample mean?110) for a random sample of size n = 10 has
a higher probability. As n increases, the standard deviation
decreases.

D. P(90?sample mean?110) for a random sample of size n = 20 has
a higher probability. As n increases, the standard deviation
increases.

A. P(90?sample mean?110) for a random sample of size n = 20 has
a higher probability. As n increases, the standard deviation
decreases.

A. P(90?sample mean?110) for a random sample of size n = 20 has
a higher probability. As n increases, the standard deviation
decreases.

B. P(90?sample mean?110) for a random sample of size n = 10 has
a higher probability. As n increases, the standard deviation
increases.

B. P(90?sample mean?110) for a random sample of size n = 10 has
a higher probability. As n increases, the standard deviation
increases.

C. P(90?sample mean?110) for a random sample of size n = 10 has
a higher probability. As n increases, the standard deviation
decreases.

C. P(90?sample mean?110) for a random sample of size n = 10 has
a higher probability. As n increases, the standard deviation
decreases.

D. P(90?sample mean?110) for a random sample of size n = 20 has
a higher probability. As n increases, the standard deviation
increases.

D. P(90?sample mean?110) for a random sample of size n = 20 has
a higher probability. As n increases, the standard deviation
increases.

Question 3 of 13
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Question 3 of 13
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Question 3 of 13
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Question 3 of 13 1.0 Points The average score of all golfers for a particular course has a
mean of 61 and a standard deviation of 4.5. Suppose 81 golfers
played the course today. Find the probability that the average
score of the 81 golfers exceeded 62.

A. .1293

B. .4772

C. .3707

D. .0228

A. .1293

B. .4772

C. .3707

D. .0228

A. .1293

A. .1293

B. .4772

B. .4772

C. .3707

C. .3707

D. .0228

D. .0228

Question 4 of 13
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Question 4 of 13
1.0 Points

Question 4 of 13
1.0 Points
Question 4 of 13 1.0 Points It has been reported that 40% of U.S. Workers employed as
purchasing managers are females. In a simple random sample of U.S.
Purchasing managers, 70 out of the 200 are females. Given this
information, what is the population proportion,??

A. 0.35

B. 0.40

C. 0.14

D. 0.70

A. 0.35

B. 0.40

C. 0.14

D. 0.70

A. 0.35

A. 0.35

B. 0.40

B. 0.40

C. 0.14

C. 0.14

D. 0.70

D. 0.70 I know the answers to all, but I just need work showing me how

General guidance

Concepts and reason
Proportion: A fraction of the total that represents a particular feature is termed as proportion. In other words, the number of occurrences of certain characteristic divided by the total number of all characteristic is termed as proportion.
Population proportion: If the proportion is computed for population it is termed as population proportion and is denoted by p.
Sample proportion: If the proportion is computed for sample it is termed as sample proportion and is denoted by .
Sampling Distribution of Proportion: The random sample of size n is taken from the population with sample proportion.
The sampling distribution of proportion has mean and the standard deviation. Moreover, the sample distribution of proportion follows normal distribution for large sample size n.
Normal distribution:
Normal distribution is a continuous distribution of data that has the bell-shaped curve. The normally distributed random variable x has meanand standard deviation.
Also, the standard normal distribution represents a normal curve with mean 0 and standard deviation 1. Thus, the parameters involved in a normal distribution are mean and standard deviation.
Standardized z-score:
The standardized z-score represents the number of standard deviations the data point is away from the mean.
• If the z-score takes positive value when it is above the mean.
• If the z-score takes negative value when it is below the mean
Central limit theorem:
The population of any distribution, the distribution of the sample means approaches a normal distribution the sample size increases. Moreover the main population follows normal then for any sample size n, the sample means is normally distributed.

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Fundamentals

population standard deviation.
Population proportion,
Sample proportion,
Let , then the standard z-score is found using the formula given below:

Where, denotes the sample mean, denotes the population mean and denotes the population standard deviation.

Step-by-step

Step 1 of 3

(1)
The population proportion and sample proportion cannot be same as population consists of whole observations but sample consists only part of the population. This indicates it is not possible that population and sample proportion has the same value.

Part 1
Thus, the statement ‘population proportion and sample proportion always has the same value’ is false.

The statement ‘population proportion and sample proportion always has the same value or not is obtained by the concept of sample and population proportion.

Use the concept of normal distribution and standard deviation to determine which has a higher probability in for a random sample of size and for a random sample of size

Step 2 of 3

(2)
Whether the probability value is large or small depends on the sample size. If there are any changes in the sample size, then the standard deviation value and probability value are affected. if the sample size is small the sample standard deviation will be closer the center of the tail and leads to the higher probability value. Also if the sample size is large the sample standard deviation will be far from the center of the tail and leads to the lower probability value.

Part 2
for a random sample of size has a higher probably. As n increases, the standard deviation decreases.

Which has a higher probability in for a random sample of size and for a random sample of size is obtained by the concept of standard deviation and normal distribution.

Use to find the probability that the average score of the 81 golfers exceeded 62.

Step 3 of 3

(3)
The probability that the average score of the 81 golfers exceeded 62 is obtained below:
Let X denotes the all golfers which follows normal distribution with mean 61 and the standard deviation of 4.5. and sample size That is,
Consider,

From the “standard normal table”, the area to the left of is 0.9772.

Part 3
Thus, the probability that the average score of the 81 golfers exceeded 62 is 0.0228.

The probability that the average score of the 81 golfers exceeded 62 is obtained by finding the probability of z less than or equal to 2.0 from the standard normal table.
The probability of is obtained by, taking the value that is intersected with the row containing the value 2.0 and the column containing the value ‘.00’, from the standard normal table. It is expected that 2.28% times that a random sample of 81 golfers played exceeded 62.

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Using z-score , then the standard z-score is found using the formula is wrong. Using z-score , then the standard z-score is found using the formula is correct.

Part 1
Thus, the statement ‘population proportion and sample proportion always has the same value’ is false.

Part 2
for a random sample of size has a higher probably. As n increases, the standard deviation decreases.

Part 3
Thus, the probability that the average score of the 81 golfers exceeded 62 is 0.0228.

Part 1
Thus, the statement ‘population proportion and sample proportion always has the same value’ is false.

Part 2
for a random sample of size has a higher probably. As n increases, the standard deviation decreases.

Part 3
Thus, the probability that the average score of the 81 golfers exceeded 62 is 0.0228.

p(1-P)
p=
X~NH
X-u Z =-
P(90
n=10
P(90
n=20
P(90
n=10
P(90
n=20
X-u Z =-
n=81
u=61,0 =4.5
P(X>62) =1-P(XS62) ( 181 181 =1-r(osás) =1-P(252)
P(X>62)=1-P(252) = 1-0.9772 = 0.0228
zs 2.0
X~NH
X-u Z =
X~NH
X-u Z =-
P(90
n=20
P(90
n=20
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