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Homework -
Hypothesis Testing: Continuous Variables (2 Sample)

DIRECTIONS: When computation is required, show all work neatly. Feel free to use some creativity in the analytical approach you take. As usual, do the problems by hand as well as with Minitab. Attach the (marked up) Minitab output showing that you know what is relevant to look at in the output, how it helps you to make the relevant decisions, and whether it agrees with your hand calculations.

Essay (15 points)

  1. Describe in your own words what Minitab means when it refers to the data as being in a single column or in different columns when doing a two-sample t test.

Multiple Choice (10 points)

  1. The statistic t is only employed when
    a. N is large.
    b. N is small.
    c. the sample standard deviation is known.
    d. the population standard deviation is known.
    e. the population standard deviation is unknown.

  2. As the alpha level becomes more conservative (e.g., .01 rather than .05), the critical value of t will
    a. decrease.
    b. increase.
    c. remain the same.
    d. insufficient information is given.

Problems (Please use the 6 step procedure for doing hypothesis tests that we use in class.)

  1. A random sample of a dozen Wisconsinites drink an average of 4.9 drinks per week with a standard deviation of 2.3, while a similar sample of New Yorkers only drink 3.7 drinks per week with a standard deviation of 2.1. Do the people in these two states differ in their drinking behavior? Note, just do this by hand. In other words, I am not requiring Minitab for this problem. (25 points)

  2. In a study aimed at determining the effectiveness of a new diet, an insurance company selects a sample of nine overweight men between the ages of 40 and 50 and obtains their weight measurements both before the diet begins and sixty days after it is instituted. Given the data below, is the diet effective? (25 points)

    SUBJECT
    1
    2
    3
    4
    5
    6
    7
    8
    9
    Before
    202 237 173 161 185 210 209 191 209
    After
    180 221 175 158 180 197 205 196 185

  3. In the study above, an extraneous variable is the fact that subjects may lose weight during the 60 day time period for reasons other than the diet. Therefore, we decide to include a control group. This group will be matched in weight to the experimental subjects, but will not receive the diet. Their data is given below. Is the diet effective? Feel free to be creative in your solution to this problem because there are multiple ways of solving based upon what we have learned so far. (25 points)

    SUBJECT
    1
    2
    3
    4
    5
    6
    7
    8
    9
    Before
    203 235 175 159 183 210 209 192 201
    After
    207 231 172 164 187 204 215 215 184
      

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