Hypothesis Tests for two Means, Two Variances, or Two Proportions Suggested Problems

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Hypothesis Tests for two Means, Two Variances, or
Two Proportions Suggested Problems
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Barnes 10.1

• The ductility of metal bar stock is an important
  property of the raw material for companies
  engaged in extrusion manufacturing, such as in
  the making of electrical conduit. It is equally
  important that the metal be neither too ductile
  nor not ductile enough. Two suppliers currently
  provide raw materials to your company. A sample
  of 14 bars is taken from the inventory of each
  suppliers product, and the average ductilities
  from the samples are x-bar1 46 and x-bar2 53.
  The standard deviation of each meausre is known
  to be ?1 5 and ?2 7. Based on this
  information, determine if there is a significant
  difference in ductility between the two products.

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Barnes 10.1

• Solving by hand
• H0 p .50
• H1 p gt .50
• n (50)1000 500
• Confidence level 99
• Z? Z.01 2.3268
• The rejection region is z gt za z.01 2.3268
• The sample proportion is
• The value of the test statistic is

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Barnes 10.2

• Two companies sell varnish to the general public.
  Seventeen cans of vendor As product and 12 cans
  of vendor Bs product are purchased at random
  locations. Each cans contents are used to paint
  a 1-square foot area on a test board, and the
  drying time for each sample is measured and
  recorded. The following results have been
  obtained x-barA 20, x-barB 24, sA 3.5, and
  sB 5.0. If it is important that Bs product not
  take longer than As to dry, determine if this
  data set implies a significant difference in
  drying times between the two products.

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Barnes 10.3

• Determine if a significant difference exists
  between the variables of the two populations
  studied in Exercise 10.2.

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Barnes 9.12

• Solving by hand
• H0 ? 90.50
• H1 ? lt 90.50
• n 22, x-bar 89, s 3
• Confidence level 95
• The rejection region is t lt ta,n 1 t .05,
  22-1 1.721
• The value of the test statistic is

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Barnes 10.7

• The Field Research Group of the Indianapolis
  Branch Laboratory of the Day, Tee, and Tee
  Development Corporation is chared with not
  allowing any cost-reduced product to be put into
  the field before it has been shown to be at least
  as reliable as the product thart it is replacing.
  Because all items that DTT provides to its
  customers are on a lease-only basis, it is
  possible to obtain very good records in regard to
  the number of products of a particular type that
  have experienced any difficulty. The Illinois
  branch of DTT agreed to allow a field test of
  the comparison, two samples of 1000 each of the
  old Autocaller 1.0 and the new Autocaller 2.0 are
  put into service in Illinois customers homes.
  After 6 months, 52 of the old units and 66 of the
  new units have required repair operations. What
  may we conclude about the relative reliability of
  the two products? If we are interested in being
  able to detect a difference of .75, what is your
  opinion of the sample sizes that were used?

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Barnes 9.19

• A producer of brass rivets claims that its rivets
  diameters have ? .01 inch. A sample of 10
  rivets has s .018. What can you conclude about
  the rivet makers claim? Is the sample adequately
  sized to make any decision?

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Example 9.19

• Solving by hand
• H0 ?2 .0001
• H1 ?2 gt .0001
• n 10, s .018
• Confidence level 95

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Example 9.19

• Since 29.16 gt 3.325, then reject the null
  hypothesis, thus the brass rivet producers claim
  is not accurate

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Barnes 9.25

• The proportion of people missing a particular
  class day must be less than .25. A sample of 100
  days is taken, yielding an average proportion of
  .23. What is your conclusion?

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Barnes 9.25

• Solving by hand
• H0 p .25
• H1 p lt .25
• n 100
• Confidence level 99
• Z? Z.01 2.3268
• The rejection region is z lt za z.01 2.3268
• The sample proportion is
• The value of the test statistic is

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Barnes 9.25

• Since 4.6188 lt 2.3268, then reject the null
  hypothesis