An Apple A Day

1
An Apple A Day

• Amy Harpenau
• Heather Brown
• Nikki Beneigh
• Jason Allen

2
Population

• A population is the collection of all outcomes,
  responses, measurements, or counts that are of
  interest.
• Our population is the FCHS faculty (that
  responded to our survey).

3
Sample Size

• A sample is a subset of the population.
• Our sample size is 16

Type of Sample

• Systematic Sample - sample in which each member
  of the population is assigned a number. The
  members of the population are ordered in some
  way, a starting number is randomly selected, and
  then sample members are selected at regular
  intervals from the starting number.

4
Type of Sample cont.

• We arranged them in ascending order, started with
  the second survey, and selected every other
  survey from that point forward.
• This is our sample
• 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 5, 10, 210
• Mean 13.73
• Median 2
• Mode 0

5
Qualitative Data

• Qualitative data consists of attributes, labels,
  or nonnumerical entries.
• We asked FCHS faculty the following questions.
• Are the majority of the gifts you receive from
  students apple items?
• Do you collect apples or just accumulate them?

6
Results

• Question 1
• 1 faculty member receives mostly apple items
  from students
• 15 faculty members said that the majority of
  their gifts from students were not apple items.
• Question 2
• 1 teacher collects apples items
• 6 teachers accumulate their apple items
• 8 teachers do not collect or accumulate apples
• 1 teacher collects and accumulates apples

7
Quantitative Data

• Quantitative data consists of numerical
  measurements or counts.
• We asked FCHS faculty the following question
• How many apple items do you own?

8
Results

• 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2,
  2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 5, 5, 5, 6, 10, 20,
  210

Population Mean 9.09 Population Median
2 Population Mode 0
9
Level of Measurement

• Qualitative Data Nominal
• Data at the nominal level of measurement are
  qualitative only. Data at this level are
  categorized using names, labels, or qualities.
  No mathematical computations can be made at this
  level.

• Quantitative Data Interval
• Data at the interval level of measurement are
  quantitative. The data can be ordered and you
  can calculate meaningful differences between data
  entries. Zero is counted as a data entry.

10
Calculating An Outlier

• An outlier is mathematically defined as a piece
  of data with a z-score greater than 3.5 or less
  than -3.5.
• The sample mean is subtracted from the selected
  data piece. Then the answer is divided by the
  standard deviation of the sample to determine its
  z-score.
• (210 13.73) / 49.04 4.00
• 4.00 gt 3.5

11
Outliers

• You can observe from our data set that there is 1
  piece of extraneous data.
• 210
• This piece of data is an outlier and will be
  thrown out.
• (An outlier is a piece of data that is far
  removed from the data set)

12
Standard Normal Distribution
13
Pie Chart On Sample Data
14

• Box and Whisker Plot

15
Frequency Distribution
16
Frequency
17
Relative Frequency
18
Probability

• The probability of a teacher within our sample
  having exactly 0 apples is 33 (5/15)
• The probability of a teacher within our sample
  having exactly 1 apple is 13 (2/15)
• The probability of a teacher within our sample
  having more than 1 apple is 53 (8/15)

19
Hypothesis Testing

• Claim A randomly selected teacher from the
  sample will have at least one apple.
• Ho 1
• Ha lt 1
• Left tailed
• (derived from alternative hypothesis)
• Claim

20
Hypothesis Testing Cont.

• Sample n 15
• Degree of Freedom 15 1 14
• t - 1.761
• X 2.07
• ? .05
• ? 2.48

21
Hypothesis Testing Cont.
(2.07 1) / (2.48/v(15)) 1.67
z-score p-value of the z-score .9415 If p is
greater than ?, we fail to reject the null. Since
.9415 is greater than .05 we have to fail to
reject the null which is the claim.

• The claim or null hypothesis is statistically
  correct.

22
In conclusion

• Contrary to popular belief, teachers dont
  frequently collect or receive apples from their
  students.