Comparing Two Means

1
Unit 17

• Comparing Two Means
• Independent Samples

2
Comparing Means

• Experiments comparing means are common in science
  and industry.
• Compare the effects of a new drug with
  traditional treatment
• Compare the fuel efficiencies of two engines
• Compare the sales of a product in two different
  cities

3
Estimating Differences

• The confidence interval for the difference
  between means of two independent groups,
  is
• The computational formula for the SE depends on
  the samples sizes and the standard deviations

4
On the TI-83/84

• Select 02-SampTInt from the STAT TESTS menu
• If the data is in list select Data, enter the two
  lists, and set frequency to 1
• If the summary statistics are known select Stats
• Enter the mean, standard deviation and sample
  size for sample 1 followed by sample 2
• Specify the confidence level
• Pooled Yes
• Calculate

5
Brand Name or Generic

• Do brand name and generic AA batteries have
  different mean lifetimes. The data in the table
  was collected on six pairs of AA batteries used
  under the same conditions.
• Lifetime in minutes

6
Solution

• The 95 CI is
• Rewriting to make the quantities positive
• We are 95 confident that on average generic AA
  batteries last between 2.3 and 34.9 minutes
  longer than the brand name AA batteries.

7
Two Sample t-test

• To test that there is no difference between the
  means of two independent groups
• Test the null hypothesis
• Use the test statistic

8
On the TI 83/84

• Select 42-SampTTest from the STAT TESTS menu
• If the data is in list select Data, enter the two
  lists, and set frequency to 1
• If the summary statistics are known select Stats
• Enter the mean, standard deviation and sample
  size for sample 1 followed by sample 2
• Specify the form of the alternative hypothesis
• Pooled Yes
• Calculate

9
Batteries

• Test the null hypothesis of no difference in
  battery life between brand name and generic
  batteries. Use a two-tailed alternative.
• Interpret your result

10
Solution

• Reject Ho. Since the t value is negative and
  brand name batteries were sample 1 we conclude
• Brand name batteries have a shorter life than
  generic batteries (plt.03)

11
Learning Math

• CPMP is an innovative approach to teaching
  math that engages students in group
  investigations. Scores on an applied algebra test
  where students were allowed to use calculators
  were compared for CPMP students and students
  taking a traditional algebra course. Compare the
  programs.

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Solution

• Reject Ho. On average students in the traditional
  program scored higher than those in the CPMP
  program (plt.0001)
• 95 confidence interval
• On average students in the traditional program
  scored between 6.5 to 12.3 points higher than the
  CPMP program

13
Pulse Rates

• A researcher wants to see whether there is a
  significant difference in pulse rates for men and
  women. The data is summarized below. Analyze the
  data

14
Solution

• Keep Ho. There is no evidence of a significant
  difference in the average pulse rates of men and
  women
• 95 CI
• With 95 confidence we cannot state there is a
  difference between the pulse rates of men and
  women

15
Salaries

• A researcher wants to determine if the starting
  salaries of MIS majors differ from those of
  accounting majors. She collected salary data on
  randomly selected who graduated in 2004. Analyze
  the data.

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Solution

• Reject Ho. On average MIS majors graduating last
  year made significantly higher salaries than
  accounting majors (plt.0001)
• 95 CI
• On average MIS starting salary is from 3261 to
  3617 higher than accounting majors