business statistics exam on t-test
muaya
QMET251TESTONt-testswith2setsofsampledataSPRING2020.docQMET 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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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?
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b. How many tails does this problem have?______________
c. What is the table value (put the actual number) , and what is its sign?_____________
d. What is the DCAR statement for this problem?
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5. A new breakfast cereal is being test-marketed in selected cities on the east and west coasts. Consumer panels are being used for the evaluation in each of the selected cities; and, after four weeks of product use, the consumer reactions have been obtained as follows:
East Coast West Coast
Total number of responses 630 425
Preferred the new cereal 425 385
Considered the cereal inferior to others 205 40
Past test-marketing experience indicates that at least seventy-eight percent consumer panel acceptance must be demonstrated before a product has a chance to be successful. There is also interest in determining whether there are regional differences in consumer acceptance of the product. To answer this question of regional differences, a test of hypothesis was conducted between the preferences of the panels on the East and West coasts, at the one percent level of significance, and the computed value for this test was
-8.7283.
a. What is the null hypothesis?
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b. Is this a one- or a two-tail test? __________
c. What is the table value, what is its size (i.e., what is the number???) and its sign?____________
d. What is the DCAR statement for this problem?
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6. Research is being conducted to determine which gender (males or females, in case any of you are confused) makes the greatest proportionate use of shopping lists when doing their grocery shopping. A sample of two thousand females found eight hundred who use such lists, and a similar sample of one thousand males found three hundred used shopping lists. If the ten percent alpha level was used, and the computed value was found to be +5.360493, can we safely conclude that a larger percentage of women use grocery shopping lists than do men?
a. What is the null hypothesis for this problem?
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b. Is this a one- or a two-tailed test?____________
c. Is the table value a t or z, and what is it (put the actual number!) and its sign? ______________
d. What is the DCAR statement? __________________________________
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