Summary (Large Sample Sizes)

1
Summary (Large Sample Sizes)
Degree of confidence
Critical value(from the z table)
Sample standard deviation (s) Sample size (n)
Intervalestimate
Sample mean
2
Critical Value

• Using the standard normal distribution (z-table)
  for the critical value works for large (gt 30)
  sample sizes
• For smaller sample sizes, we use the Student
  distribution (t table, A-3)
• For that, we need the
• The number of degrees of freedom, and
• a, which is (1 degree of confidence)
• Using these two values, we look up the t
  distribution value in the table A-3
• The t-score becomes the critical value we use to
  find the margin of error.

3
Degrees of Freedom

• The sample size, n, minus 1 (n 1)
• Based on the concept that in a sample of n items
  in which we know the mean, the first (n 1)
  values can be anything the nth sample must then
  be what ever is necessary to give the resulting
  mean.

4
Summary (Small Sample Sizes)
Degree of confidence and sample size
Critical value(from the t table)
Sample standard deviation Sample size
Intervalestimate
Sample mean
5
For example

• The average math SAT score in our opinion poll
  was 670 the standard deviation is 87. Calculate
  an interval estimate for the entire population
• Degree of confidence
• alpha
• Sample size
• Degrees of freedom
• t score ta/2
• Margin of error (E)
• Interval

6
Summary (Small Sample Sizes)
Degree of confidence and sample size
Critical value(from the t table)
Sample standard deviation Sample size
Intervalestimate
Sample mean
7
Live example

• The average height of the 12-man basket ball team
  is 70, the standard deviation is 4.5
• Degree of confidence
• alpha
• Sample size
• Degrees of freedom
• t score ta/2
• Margin of error (E)
• Interval

8
Summary (Small Sample Sizes)
Degree of confidence and sample size
Critical value(from the t table)
Sample standard deviation Sample size
Intervalestimate
Sample mean
9
Your turn

• My 2nd period algebra class of 23 has a mean
  average of 83 the standard deviation is 7.
  Calculate an interval estimate for the entire
  population
• Degree of confidence
• alpha
• Sample size
• Degrees of freedom
• t score ta/2
• Margin of error (E)
• Interval

10
Summary (Small Sample Sizes)
Degree of confidence and sample size
Critical value(from the t table)
Sample standard deviation Sample size
Intervalestimate
Sample mean
11
Homework

• Find the margin of error and interval estimate
  for the following point estimates

X-bar s n Degree of confidence E Interval
25 1.3 15 90
165 8.5 26 95
570 101 14 99
0.59 0.09 22 95
12650 1750 29 95
12
More Homework

• 15 students have cars that are worth an average
  9,500 (standard deviation is 2,100) and average
  27.5 MPG (standard deviation is 6.9).
• Use this poll to find the interval estimate for
  value
• Find the interval estimate for MPG
• 8 students have an average GPA of 3.6 (standard
  deviation is 1) Use this poll to find the
  interval estimate for GPA
• Find the interval estimate for MPG