Please i really need help with thus on Complete the following: A new college is
ID: 427344 • Letter: P
Question
Please i really need help with thus on
Complete the following: A new college is looking for housing for their potential students. Below is a table for how many persons a sample of potential buildings can house. Using this table, calculate the sample mean and sample standard deviation for maximum capacity of for these venues. Looking at these values, about 68% fall between ___ and ___, about 95% fall between ___ and ____, and about 99% fall between ___ and ___.
50
45
65
43
63
23
55
44
34
54
65
34
34
65
66
34
34
54
55
35
63
34
23
23
26
45
33
35
67
68
43
63
23
55
54
59
50
58
58
57
65
66
34
34
55
30
26
45
33
47
38
26
45
33
67
43
63
23
55
48
37
39
40
30
39
65
66
34
34
49
38
38
59
26
45
33
40
45
47
55
4. Create two different graphs using Excel to display this data. One must be the normal distribution curve
5. Write a scenario that this data may represent. It does not have to be a factual scenario.
50
45
65
43
63
23
55
44
34
54
65
34
34
65
66
34
34
54
55
35
63
34
23
23
26
45
33
35
67
68
43
63
23
55
54
59
50
58
58
57
65
66
34
34
55
30
26
45
33
47
38
26
45
33
67
43
63
23
55
48
37
39
40
30
39
65
66
34
34
49
38
38
59
26
45
33
40
45
47
55
Explanation / Answer
General Objective: In inferential statistics, we want to use characteristics of the sample (i.e. a statistic) to estimate the characteristics of the population (i.e. a parameter). What happens when we take a sample of size n from some population? If a continuous distribution, how is the sample mean distributed?&fnbsp; If taken from a categorical population set of data, how is that sample proportion distributed? One uses the sample mean (the statistic) to estimate the population mean (the parameter) and the sample proportion (the statistic) to estimate the population proportion (the parameter). In doing so, we need to know the properties of the sample mean or the sample proportion. That is why we need to study the sampling distribution of the statistics. We will begin with the sampling distribution of the sample mean. Since the sample statistic is a single value that estimates a population paramater, we refer to the statistic as a point estimate.
Before we begin, we will introduce a brief explanation of notation and some new terms that we will use this lesson and in future lessons.
Notation:
Sample mean: book uses y-bar or
¯
y
y; most other sources use x-bar or
¯
x
x
Population mean: standard notation is the Greek letter
?
?
Sample proportion: book uses ?-hat (
^
?
?); other sources use p-hat, (
^
p
p)
Population proportion: book uses
?
?; other sources use p
[NOTE: Remember that the use of
?
? is NOT to be interpreted as the numeric representation of 3.14 but instead is simply a symbol.]
Terms
Standard error – standard deviation of a sample statistic
Standard deviation – relates to a sample
Parameters, e.g. mean and SD, are summary measures of population, e.g.
?
? and
?
?. These are fixed.
Statistics, e.g. sample mean and sample SD, are summary measures of a sample, e.g.
¯
x
x and s. These vary. Think about taking a sample and the sample isn’t always the same therefore the statistics change. This is the motiviation behind this lesson - due to this sampling variation the sample statistics themselves have a distribution that can be described by some measure of central tendency and spread.
Sampling Distribution of the Sample Mean
A large tank of fish from a hatchery is being delivered to the lake. We want to know the average length of the fish in the tank. Instead of measuring all the fish, we randomly sample some of them and use the sample mean to estimate the population mean.
Note: The sample mean
¯
y
y is random since its value depends on the sample chosen. It is called a statistic. The population mean is fixed, usually denoted as
?
?.
The sampling distribution of the (sample) mean is also called the distribution of the variable
¯
y
y.
Usually, the sampling distribution of the sample mean is complicated except for very small sample size or for large sample size. In the following example, we illustrate the sampling distribution for a very small population. The sampling method is to sample without replacement.
Example: Pumpkin Weights
The population is the weight of six pumpkins (in pounds) displayed in a carnival "guess the weight" game booth. You are asked to guess the average weight of the six pumpkins by taking a random sample without replacement from the population.
Pumpkin
A
B
C
D
E
F
Weight (in pounds)
19
14
15
9
10
17
a. Calculate the population mean
?
?.
?
? = (19 + 14 + 15 + 9 + 10 + 17 ) / 6 = 14 pounds
b. Obtain the sampling distribution of the sample mean for a sample size of 2 when one samples without replacement.
Sample
Weight
¯
y
y
Probability
A, B
19, 14
16.5
1/15
A, C
19, 15
17.0
1/15
A, D
19, 9
14.0
1/15
A, E
19, 10
14.5
.
A, F
19, 17
18.0
.
B, C
14, 15
14.5
.
B, D
14, 9
11.5
.
B, E
14, 10
12.0
.
B, F
14, 17
15.5
.
C, D
15, 9
12.0
.
C, E
15, 10
12.5
.
C, F
15, 17
16.0
.
D, E
9, 10
9.5
.
D, F
9, 17
13.0
1/15
E, F
10, 17
13.5
1/15
Distribution of
¯
y
y:
¯
y
y
9.5
11.5
12.0
12.5
13.0
13.5
14.0
14.5
15.5
16.0
16.5
17.0
18.0
Probability
1/15
1/15
2/15
1/15
1/15
1/15
1/15
2/