Description

QMET 251 Second Test on t-tests

1.  In the past, a utility company sent out monthly statements to its customers without addressed return envelopes.  From a random sample of one hundred twenty old accounts, the billing department determined that, on the average, it takes nine days for a payment to return, with a standard deviation of four days.  Hoping to speed up this return time, the billing department decides to enclose pre-addressed envelopes with the invoices.  A random sample of one hundred thirty customers indicates that with the new procedure, the average payment period is now eight days with a sample standard deviation of four and eight-tenths days.  Assume that the computed value is +1.7947 and that the confidence coefficient is ninety-eight percent, and answer the following questions.

a.  What is the null hypothesis for this problem (use only one sentence, but be thorough and correct, and do not use symbols!!)?

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b.  Is this a one-tail or two-tail test?_______________

c.  Is the table value in this problem a table t or table z, and put its size (the actual table value) and its sign. __________

d.  What is the DCAR statement for this problem?

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2.  A study was being conducted of the annual incomes of probation officers in metropolitan areas having populations of less than one hundred thousand and in those areas with populations of more than five hundred thousand.  The following sample statistics were calculated:

                               Population less   Population more

                               than 100,000      than 500,000  

Sample size                          25                 60

Sample mean                        $11,290      $11,330

Sample variance                    $ 1,060      $ 1,900

We test the hypothesis that the annual incomes of probation officers in areas  with populations of more than 500,000 are significantly more than those in areas of less than 100,000, at the five percent level of significance, and calculate a computed value in step 4 of -4.648.

a.  What is the null hypothesis for this problem?

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b.  How many tails does this problem have? ________

c.  Is the table value a z- or t-value, and what is it (what is the actual number ??) and its sign? ______________

d.  What is the DCAR statement for this problem?

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3.  One of the old theories in major league baseball is that, in order to win a pennant a team has to win about seventy-five percent of its home games and about fifty percent of its games away from home.  After the first few weeks of the season, the Mudtown Sloppers have eight wins and four losses at home, and six wins and five losses on the road.  If we use the five percent level of significance, and we get a computed value to be +.59, can we conclude that the Sloppers are more sloppy on the road than at home?  Use this information to answer the following questions.    

a.  What is the null hypothesis for this problem?

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b.  How many tails does this problem have?__________

c.  What is the table value (z or t), what is it (put the actual number) , and what is its sign(s)? __________

d.  What is the DCAR statement for this problem?

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