Minitab Lab Session

1
Minitab Lab Session 3w/Homework Problems

• t confidence interval for means
• t hypothesis test for mean (one sample)
• Two population hypotheses testing
• Independent samples
• Dependent samples
• Click here for the Minitab worksheet

2
t confidence interval hypothesis test mean,
one population, ? unknown

• The following data show the number of the number
  of tickets issued by the South Boro Police each
  day for a period of a month.
• The data is in column Tickets
• Example 1
• Find a 95 confidence interval for the true mean.
• Draw a boxplot that shows the confidence interval
• A motorist claims that the South Boro Police
  issue an average of 55 speeding tickets per day.
  Perform a hypothesis test to determine whether
  there is enough evidence to support the motorists
  claim with a .05.

3
t confidence interval hypothesis test mean,
one population, ? unknown

• Homework Problem 1
• Jack works at a store that makes copies (e.g.
  Kinkos) He has recorded the number of pages
  copied by 50 randomly selected customers.
• The data is in column StoreMgr
• Find a 90 confidence interval for the true mean.
  
• Interpret the interval.
• Provide a boxplot that includes the confidence
  interval

4
t hypothesis Testing mean, one population, ?
unknown, n lt 30

• Homework Problem 2
• From past experience, a teacher believes that the
  average score on a real estate exam is 75. Data
  from 20 randomly selected students who took the
  exam recently appears below. Test the claim
  that the mean score is still 75 with ? .05.
• Assume scores are normally distributed.
• The data appears above and in Column Teacher
• Testing the claim means doing the steps in a
  hypothesis test (e.g. identifying the population
  parameter, stating the hypothesis, interpreting
  the results). Minitab computes the test
  statistic and the P-value for you.

5
Comparing two means

• H0 ?1 ?2
• Ha ?1 gt ?2 or ?1 lt ?2 or ?1 ? ?2
• The testing of these hypotheses is similar to the
  tests for a single population
• The difference is in the computation of the test
  statistic (t-value)

6
Independent versus paired samples

• Independent samples
• Two samples are independent if the selection of
  the individuals or objects that make up one
  sample does not influence the selection of the
  individuals or objects in the other sample
• For independent samples, use the Two-Sample t
  Test
• Pooled variances when unknown but equal standard
  deviations
• Unpooled variances when unknown and unequal
  standard deviations

7
Independent versus paired samples

• Paired samples
• Two samples are paired when observations from the
  first sample are paired in some meaningful way
  with observations in the second sample
• For paired samples, use the Paired t-test

8
Two sample t-test two

• Example
• Has the PH level of our nations lakes increased?
  Columns PHHist and PHCurnt are randomly
  selected samples of the PH values in US lakes.
  Perform a hypothesis test to determine whether
  the data supports the claim that the PH level of
  our nations lakes has increased. Test at the .05
  significance level
• Homework Problem 3
• A sports analyst wishes to determine whether gate
  attendance has increased from the time the San
  Francisco Giants baseball team moved to Oakland.
  Gate attendance figures (thousands) from the
  1958-1967 seasons, when the team was in San
  Francisco, and for 1968-1978 when the team was in
  Oakland appear in Columns 1958-67 and
  1968-78. Perform a hypothesis test to
  determine whether the data support a claim that
  gate attendance has increase. Use a .10
  significance level.
• See note on Homework Problem 2.

9
Paired t-test

• Example
• Are all discount mail-order companies the same?
  Data were collected on the prices of the top ten
  business software packages reported by PC
  Magazine in August 1997. Two well-know
  mail-order companies were sampled. The data are
  in Columns Comp and PCC of todays data file.
• Set up a hypothesis test to determine whether the
  average price for software is different at the
  two mail-order companies. Assume the populations
  are approximately normally distributed and a .05
  significance level.