E7'3 p343 Hypothesis test steps

1
E7.3 p343 Hypothesis test steps

• 1. State the null hypothesis, Ho. (stated in
  statistical terms)
• 2. State the alternative hypothesis, H1.
• 3. Choose the level of significance, alpha.
• (This along with the sample size, determines ß)
• 4. Choose the sample size, n.
• Sample size is determined after taking into
  account the specified risks of committing Type I
  and Type II errors i.e., selected levels of alpha
  and ß
• 5. Determine the appropriate statistical
  technique and corresponding test statistic to
  use.
• (? known ? Z test) (? unknown ? t test)
• 6. Collect the data and compute the sample value
  of the appropriate test statistic.
• 7. Calculate the p-value based on the test
  statistic.
• 8. Compare the p-value to alpha
• 9. Make the statistical decision
• reject Ho if p-value lt alpha
• fail to reject Ho if p-value gt alpha
• 10. Express the statistical decision in terms of
  the problem.
• 11. Put it all in a picture.

2

• Book example p343. Is the population mean weight
  of cereal per box different from at 368 grams?
• 1) Ho ? 368 grams
• 2) H1 ? ? 368 grams
• 3) alpha .05
• 4) n 25
• 5) ? 15 grams, so ? is known, use Z-test,
  normal distribution.
• 6) Collect data and calculate test statistic
• X-bar 372.5 grams. e7.1, p340 Z (Xbar -
  ?)/(?/n½) 1.50
• 7) Calculate the p-value
• Phstat One-Sample Tests Z test for the
  mean, ? known
• Null Hypothesis ? 368
• Level of Significance .05
• Population Standard Deviation 15
• Sample Size 25
• Sample Mean 372.5
• Two Tailed Test
• Output results p-Value .1336
• 8) p-Value .1336 gt alpha .05
• 9) Barely fail to reject Ho. Borderline
  situation. There is no evidence that the mean is
  significantly different from the hypothesized
  value.

3

• 7.30 p346. Is the average fill different from 8
  oz?
• 1) Ho ? 8 oz
• 2) H1 ? ? 8 oz
• 3) alpha .05
• 4) n 50
• 5) ? .15 oz, so ? is known, use Z-test, normal
  distribution.
• 6) Collect data and calculate test statistic
• X-bar 7.983 oz. e7.1, p340 Z (Xbar -
  ?)/(?/n½)
• Z (7.983 - 8) / ( .15 / 50½ ) -.80
• 7) Calculate the p-value
• Phstat One-Sample Tests Z test for the
  mean, ? known
• Null Hypothesis ? 8
• Level of Significance .05
• Population Standard Deviation .15
• Sample Size 50
• Sample Mean 7.983
• Two Tailed Test
• Output results p-Value .4229
• 8) p-Value .4229 gt alpha .05

4

• 7.26 p346. Is the mean break strength different
  from 70 pounds? The population standard
  deviation is 3.5 pounds.
• 1) Ho ? 70 pounds
• 2) H1 ? ? 70 pounds
• 3) alpha .05
• 4) n 49
• 5) ? 3.5 pounds, so ? is known, use Z-test,
  normal distribution.
• 6) Collect data and calculate test statistic
• X-bar 69.1 pounds. e7.1, p340 Z (Xbar -
  ?)/(?/n½)
• Z (69.1 - 70) / ( 3.5 / 49½ ) -1.80
• 7) Calculate the p-value
• Phstat One-Sample Tests Z test for the
  mean, ? known
• Null Hypothesis ? 70
• Level of Significance .05
• Population Standard Deviation 3.5
• Sample Size 49
• Sample Mean 69.1
• Two Tailed Test
• Output results p-Value .0718
• 8) p-Value .0718 gt alpha .05

5

• 7.40 p349. Are we producing bars with an average
  length of at least 2.8 feet? The population
  standard deviation is .2 feet.
• 1) Ho ? gt 2.8 feet
• 2) H1 ? lt 2.8 feet
• 3) alpha .05
• 4) n 25
• 5) ? .2 feet, so ? is known, use Z-test, normal
  distribution.
• 6) Collect data and calculate test statistic
• X-bar 2.73. e7.1, p340 Z (Xbar - ?)/(?/n½)
  
• Z (2.73 - 2.8) / ( .2 / 25½ ) -1.75
• 7) Calculate the p-value
• Phstat One-Sample Tests Z test for the
  mean, ? known
• Null Hypothesis ? 2.8
• Level of Significance .05
• Population Standard Deviation .2
• Sample Size 25
• Sample Mean 2.73
• Lower Tailed Test
• Output results p-Value .0401
• 8) p-Value .0401 lt alpha .05

6

• GMAT example. The Director of Admissions at MSU
  believes that their MBA students are above the
  national average. The population average GMAT
  score is 500 with a population standard deviation
  of 100. A sample of 12 MSU MBA students is
  selected at random. The sample mean is 537. Use
  a level of significance of .01.
• 1) Ho ? lt 500 points
• 2) H1 ? gt 500 points
• 3) alpha .01
• 4) n 12
• 5) ? 100 points, so ? is known, use Z-test,
  normal distribution.
• 6) Collect data and calculate test statistic
• X-bar 537 points. e7.1, p340 Z (Xbar -
  ?)/(?/n½)
• Z (537 - 500) / (100 / 12½) 1.28
• 7) Calculate the p-value
• Phstat One-Sample Tests Z test for the
  mean, ? known
• Null Hypothesis ? 500
• Level of Significance .01
• Population Standard Deviation 100
• Sample Size 12
• Sample Mean 537
• Upper Tailed Test
• Output results p-Value .09997
• 8) p-Value .09997 gt alpha .01

7
Problem 7.50 page 356, The director of admissions
at a large university advises parents of incoming
students about the cost of textbooks during a
typical semester. A sample of 100 students
enrolled in the university indicates a sample
mean cost of 315.40, with a sample standard
deviation of 43.20. Use a level of significance
of 0.01. Is there evidence that the population
average is above 300. 1) Ho ? lt 300 2) H1
? gt 300 3) alpha .01 4) n 100 5) ? unknown,
only sample information, t-test 6) Collect data
and calculate test statistic X-bar 315.40.
e7.2, p350 t (Xbar - ?)/(S/n½) t
(315.4 - 300) / ( 43.2 / 100½) 3.56 7)
Calculate the p-value Phstat One-Sample Tests
t test for the mean, ? unknown Null Hypothesis
? 300 Level of Significance
.01 Sample Standard Deviation 43.2 Sample
Size 100 Sample Mean 315.40 Upper Tail
Test Output results p-Value .00028 8)
p-Value .00028 lt alpha .10 9) Strongly
reject Ho. There is evidence that the mean is
significantly greater than the hypothesized
value. 10) Change our printed material. The
University can no longer claim that text books
cost 300 or less per semester. We have evidence
that the population mean is significantly greater
than 300. 11) Picture
8

• You are the manager of the Lawn and Garden
  department at Wal-mart. You sell riding lawn
  mower batteries made by XYZ corporation. XYZ
  inc. claims to produce riding lawn mower
  batteries that produce 140 amps of power or more.
  Many of your customers have returned this brand
  of battery. Should you switch suppliers? Use a
  level of significance of 0.05. A sample of 20
  batteries were tested and the results are in a
  data file called
• http//www.muw.edu/aehlert Course Material
  BU270_Stats example_files Amphrs.xls
• 1) Ho ? gt 140 amps
• 2) H1 ? lt 140 amps
• 3) alpha .05
• 4) n 20
• 5) ? unknown, only sample information, t-test
• 6) Collect data and calculate test statistic
• X-bar 138.47. e7.2, p350 t (Xbar -
  ?)/(S/n½)
• t (138.47 - 140) / ( 2.66 / 20½) -2.57
• 7) Calculate the p-value
• Phstat One-Sample Tests t test for the
  mean, ? unknown
• Null Hypothesis ? 140
• Level of Significance .05
• Sample Standard Deviation 2.66
• Sample Size 20
• Sample Mean 138.47
• Lower Tail Test
• Output results p-Value .0093

9

• Problem 7.54 page 356. Is the mean different
  from zero? A sample of 100 steel parts were
  measured and the results are in a data file
  called
• http//www.muw.edu/aehlert Course Material
  BU270_Stats example_files steel.xls
• 1) Ho ? 0 inches
• 2) H1 ? ? 0 inches
• 3) alpha .05
• 4) n 100
• 5) ? unknown, only sample information, t-test
• 6) Collect data and calculate test statistic
• X-bar -.00023. e7.2, p350 t (Xbar -
  ?)/(S/n½)
• t (-.00023 - 0) / ( .00170 / 100½) -1.36
• 7) Calculate the p-value
• Phstat One-Sample Tests t test for the
  mean, ? unknown
• Null Hypothesis ? 0
• Level of Significance .05
• Sample Standard Deviation .00170
• Sample Size 100
• Sample Mean -.00023
• Two Tail Test
• Output results p-Value .1792