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. 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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4. A random sample of sixteen large manufacturing firms indicated that the average age of the president of the firm at the time he/she became president was forty-seven years. Similarly, a random sample of sixteen medium-size manufacturing firms revealed an average age of forty-five years. The standard deviation of the large firm was fifteen years, and the standard deviation of the medium-size firms was five years. If we find the computed value to be +0.5310, with an alpha level of five percent, can we conclude that an individual has to be older to be president of a large manufacturing company than he/she does in order to be president of a medium-size manufacturing firm?

a. What is the null hypothesis here?