Question 1

Exhibit 7-1
A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces.
-Refer to Exhibit 7-1. The point estimate of the mean content of the bottles is

Accepted Answer

The point estimate of the mean content is given as the sample average, which is 4 ounces.

Question 2

Exhibit 7-2
A random sample of 10 examination papers in a course, which was given on a pass or fail basis, showed the following scores. 
-Refer to Exhibit 7-2. The point estimate for the proportion of all students who passed the course is

Accepted Answer

The point estimate for the proportion of all students who passed the course is the proportion of the sample who passed the course. In this case, 8 out of 10 students passed, so the point estimate is 8/10 or 0.8.

Question 3

The following data was collected from a simple random sample of a population. 13 15 14 16 12
The point estimate of the population mean

Accepted Answer

The point estimate of the population mean is the sample mean. Therefore, the best choice is B which is 14, the sample mean.

Question 4

The following information was collected from a simple random sample of a population. 16
19 18 17 20 18
The point estimate of the mean of the population is

Accepted Answer

To find the point estimate of the mean of the population, we simply take the average of the sample. 
(16 + 19 + 18 + 17 + 20 + 18) / 6 = 18 
Therefore, the best choice for the point estimate is A) 18.0.

Question 5

The following data was collected from a simple random sample of a population. 13 15 14 16 12
The point estimate of the population standard deviation is

Accepted Answer

To estimate the population standard deviation, we use the formula s = sqrt(Σ(xi-x̄)²/(n-1)) where x̄ is the mean of the sample, xi is each data point, and n is the sample size.

Plugging in the values from the sample, we get:

s = sqrt(((13-14.0)² + (15-14.0)² + (14-14.0)² + (16-14.0)² + (12-14.0)²) / 4)
s = sqrt((1² + 1² + 0² + 2² + (-2)²)/4)
s = sqrt(10/4)
s = sqrt(2.5)

Therefore, the point estimate of the population standard deviation is s = 1.581.

Option B is the answer.

Question 6

The following data was collected from a simple random sample of a population. 13 15 14 16 12
If the population consisted of 10 elements, how many different random samples of size 6 could be drawn from the population?

Accepted Answer

The number of different random samples of size 6 that can be drawn from a population of 10 elements is calculated using the combination formula C(n, k) = n! / (k!(n-k)!), where n is the total number of elements in the population and k is the sample size. Here, C(10, 6) = 10! / (6!4!) = 210.

Question 7

Exhibit 7-2
A random sample of 10 examination papers in a course, which was given on a pass or fail basis, showed the following scores. 
-Refer to Exhibit 7-2. The point estimate for the variance of the population is

Accepted Answer

The point estimate for the variance of the population is the sample variance, which is calculated by dividing the sum of squared deviations from the mean by the number of observations minus one. In this case, the sample variance is 419.43.

Question 8

The following information was collected from a simple random sample of a population. 16
19 18 17 20 18
The point estimate of the population standard deviation is

Accepted Answer

The answer of The following information was collected from a...

Question 9

Exhibit 7-2
A random sample of 10 examination papers in a course, which was given on a pass or fail basis, showed the following scores. 
-Refer to Exhibit 7-2. The point estimate for the mean of the population is

Accepted Answer

The answer of Exhibit 7-2
A random sample of 10 examination...

Question 10

Exhibit 7-3
In a local university, 40% of the students live in the dormitories. A random sample of 80 students is selected for a particular study.
-Refer to Exhibit 7-3. The standard deviation of  , known as the standard error of the proportion is approximately

Accepted Answer

The formula for calculating the standard error of the proportion is SEp = sqrt(pq/n), where p is the proportion of the population, q is the complement of the proportion (1-p), and n is the sample size. Given that p = 0.4, q = 0.6, and n = 80, the standard error of the proportion is calculated as SEp = sqrt(0.4*0.6/80) = 0.05477 (rounded to 5 decimal places), which corresponds to choice C.

Question 11

The following data was collected from a simple random sample of a population. 13 15 14 16 12
The mean of the population

Accepted Answer

The mean of a sample is not necessarily the mean of the entire population; it is an estimate and the population mean could be any value.

Question 12

The number of different simple random samples of size 5 that can be selected from a population of size 8 is

Accepted Answer

The number of different simple random samples of size 5 that can be selected from a population of size 8 is given by the combination formula:
C(8,5) = 8!/(5!3!) = (8x7x6)/(3x2x1) = 56

Question 13

Exhibit 7-1
A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces.
-Refer to Exhibit 7-1. The standard error of the mean equals

Accepted Answer

The standard error of the mean is calculated as the population standard deviation divided by the square root of the sample size: 0.22 / √121 = 0.02.

Question 14

Exhibit 7-3
In a local university, 40% of the students live in the dormitories. A random sample of 80 students is selected for a particular study.
-Refer to Exhibit 7-3. The probability that the sample proportion (the proportion living in the dormitories) is at least 0.30 is

Accepted Answer

We are dealing with a binomial distribution (students living in dorms or not) and the sample size (80) is large enough to use the normal approximation to the binomial distribution. The mean of the sample proportion is p = 0.40 and the standard deviation is calculated as sqrt[(p*(1-p))/n] = sqrt[(0.4*0.6)/80] = 0.06. 
To find the probability that the sample proportion is at least 0.30, we need to find the area to the right of 0.30 under the standard normal distribution. Using z-score formula, z = (0.30-0.40)/0.06 = -1.67. Consulting a standard normal distribution table or using a calculator, we find that the area to the right of -1.67 is 0.9525. However, since we want the area to the right of 0.30 (not to the left of 0.30), we subtract this value from 1: 1 - 0.9525 = 0.0475. Thus, the probability that the sample proportion is at least 0.30 is 0.0475 or 4.75%. Therefore, the best choice is (C).

Question 15

Exhibit 7-2
A random sample of 10 examination papers in a course, which was given on a pass or fail basis, showed the following scores. 
-Refer to Exhibit 7-2. The point estimate for the standard deviation of the population is

Accepted Answer

To find the point estimate for the standard deviation of the population, we use the formula:
s = √[(Σ(x - x̄)²)/(n - 1)]
Plugging in the given values, we get:
s = √[(Σ(x - x̄)²)/(n - 1)]
s = √[(17.6 + 51.84 + 5.76 + 46.24 + 11.56 + 7.84 + 2.56 + 22.09 + 75.69 + 33.64)/(10 - 1)]
s = √[275.48/9]
s = √30.61
s = 5.53
Therefore, the point estimate for the standard deviation of the population is 5.53, which corresponds to choice B.

Question 16

Exhibit 7-1
A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces.
-Refer to Exhibit 7-1. In this problem the 0.22 is

Accepted Answer

The 0.22 is a parameter because it is a numerical value that describes a characteristic of the population (the standard deviation of the contents of all cologne bottles).

Question 17

Four hundred people were asked whether gun laws should be more stringent. Three hundred said "yes," and 100 said "no." The point estimate of the proportion in the population who will respond "yes" is

Accepted Answer

The point estimate of the proportion in the population who will respond "yes" is the proportion of the sample (300) who said "yes" divided by the total sample size (400), which is 300/400 = 0.75. Therefore, the answer is C, 0.75.

Question 18

Exhibit 7-3
In a local university, 40% of the students live in the dormitories. A random sample of 80 students is selected for a particular study.
-Refer to Exhibit 7-3. The probability that the sample proportion (the proportion living in the dormitories) is between 0.30 and 0.50 is

Accepted Answer

To find the probability that the sample proportion is between 0.30 and 0.50, we first need to find the mean and standard deviation of the sampling distribution of the sample proportion. The mean of the sampling distribution of the sample proportion is equal to the population proportion, which is 0.40. The standard deviation of the sampling distribution can be found using the formula:

sqrt[(p*(1-p))/n] = sqrt[(0.4*(1-0.4))/80] = 0.0511

Next, we need to standardize the interval (0.30, 0.50) using the formula:

(z - mean)/standard deviation

where z is the standardized value, mean is the population proportion of 0.40, and standard deviation is 0.0511.

For the lower limit of 0.30:

(z - 0.40)/0.0511 = -1.96

z = -0.104

For the upper limit of 0.50:

(z - 0.40)/0.0511 = 1.96

z = 0.896

Therefore, the probability that the sample proportion is between 0.30 and 0.50 is the area under the standard normal curve between z = -0.104 and z = 0.896, which is 0.9328.

Thus, the best choice is B.

Question 19

How many different samples of size 3 can be taken from a finite population of size 10?

Accepted Answer

The number of different samples of size 3 that can be taken from a population of size 10 is calculated using the combination formula: C(n, k) = n! / [k!(n-k)!]. For this problem, C(10, 3) = 10! / [3!(10-3)!] = 120.

Question 20

Four hundred people were asked whether gun laws should be more stringent. Three hundred said "yes," and 100 said "no." The point estimate of the proportion in the population who will respond "no" is

Accepted Answer

The point estimate of the proportion in the population who will respond "no" is calculated by taking the number of people who said "no" (100) and dividing it by the total sample size (400). This gives us an estimate of 0.25 or 25%. Therefore, the best choice is B.

Quiz 7: Sampling and Sampling Distributions

Exhibit 7-1 A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces. -Refer to Exhibit 7-1. The point estimate of the mean content of the bottles is

Exhibit 7-2 A random sample of 10 examination papers in a course, which was given on a pass or fail basis, showed the following scores. -Refer to Exhibit 7-2. The point estimate for the proportion of all students who passed the course is

The following data was collected from a simple random sample of a population. 13 15 14 16 12 The point estimate of the population mean

The following information was collected from a simple random sample of a population. 16 19 18 17 20 18 The point estimate of the mean of the population is

The following data was collected from a simple random sample of a population. 13 15 14 16 12 The point estimate of the population standard deviation is

The following data was collected from a simple random sample of a population. 13 15 14 16 12 If the population consisted of 10 elements, how many different random samples of size 6 could be drawn from the population?

Exhibit 7-2 A random sample of 10 examination papers in a course, which was given on a pass or fail basis, showed the following scores. -Refer to Exhibit 7-2. The point estimate for the variance of the population is

The following information was collected from a simple random sample of a population. 16 19 18 17 20 18 The point estimate of the population standard deviation is

Exhibit 7-2 A random sample of 10 examination papers in a course, which was given on a pass or fail basis, showed the following scores. -Refer to Exhibit 7-2. The point estimate for the mean of the population is

Exhibit 7-3 In a local university, 40% of the students live in the dormitories. A random sample of 80 students is selected for a particular study. -Refer to Exhibit 7-3. The standard deviation of , known as the standard error of the proportion is approximately

The following data was collected from a simple random sample of a population. 13 15 14 16 12 The mean of the population

The number of different simple random samples of size 5 that can be selected from a population of size 8 is

Exhibit 7-1 A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces. -Refer to Exhibit 7-1. The standard error of the mean equals

Exhibit 7-3 In a local university, 40% of the students live in the dormitories. A random sample of 80 students is selected for a particular study. -Refer to Exhibit 7-3. The probability that the sample proportion (the proportion living in the dormitories) is at least 0.30 is

Exhibit 7-2 A random sample of 10 examination papers in a course, which was given on a pass or fail basis, showed the following scores. -Refer to Exhibit 7-2. The point estimate for the standard deviation of the population is

Exhibit 7-1 A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces. -Refer to Exhibit 7-1. In this problem the 0.22 is

Four hundred people were asked whether gun laws should be more stringent. Three hundred said "yes," and 100 said "no." The point estimate of the proportion in the population who will respond "yes" is

Exhibit 7-3 In a local university, 40% of the students live in the dormitories. A random sample of 80 students is selected for a particular study. -Refer to Exhibit 7-3. The probability that the sample proportion (the proportion living in the dormitories) is between 0.30 and 0.50 is

How many different samples of size 3 can be taken from a finite population of size 10?

Four hundred people were asked whether gun laws should be more stringent. Three hundred said "yes," and 100 said "no." The point estimate of the proportion in the population who will respond "no" is