Hypothesis Testing: Continuous Variables (1 Sample)
DIRECTIONS: Be sure to show the necessary calculations to back up your answers and show all work neatly. Use the six step procedure shown in class for any hypothesis tests.
Definition/Essay (6 points each)
- Describe what "sampling error" is.
- Describe what the "standard error" is.
- What does the term "critical region" refer to?
- Describe and discuss the (four possible) decisions one can make when doing a hypothesis test.
Multiple Choice (6 points each)
- In a normally distributed population with a mean of 15 and a standard deviation of 4, we draw, with replacement, samples of size N=2. Which pair of scores is LEAST likely to be selected?
a. 12, 18
b. 15, 15
c. 11, 19
d. 13, 17
e. 15, 14
- When computing a sampling distribution, the number of cases in each sample is
a. varied as the square of the variance.
b. greater than the mean.
c. less than the mean.
d. held constant.
Problems (Note that being able to figure out which are parameters and which are statistics is the key to determining what the appropriate statistical test will be.)
- An instructor gives her a class an exam which, as she knows from years of experience, yields a mean of 78 and a standard deviation of 7. Her present class of 22 obtains a mean of 82. Is she correct in assuming that this is a superior class? (10 points)
A social psychologist suggests that the average length of courtship before a second marriage is longer than before a first. He bases his suggestion on the fact that the average length of courtship before first marriages is 265 days (population value) whereas the average for second marriages (his 626 subjects) is 268.5 days with a standard deviation of 50. Is his suggestion valid? (10 points)
For the next two questions do the work by hand as well as with Minitab. Attach Minitab output and mark it up to clearly indicate the relevant material in the output that describes the data as well as helps you make a decision about it. As usual indicate whether whether the Minitab and hand calculations agree.
You strongly suspect that people are getting more creative. In the past (data from 1999) the average person scored 80 on the Smith Inventory of Creative Knowledge (SICK). The standard deviation for this population was 10. Drawing a random sample of 10 people in 2009, you obtain the following scores:
80, 88, 94, 73, 85, 89, 79, 83, 82, 85.
Using the appropriate statistical test, determine the outcome of the study:
a. Given all of the above data. (15 points)
b. Assuming trat we did not know the population standard deviation. (15 points)
- A study of reaction time of children with cerebral palsy reported an average of 1.6 seconds on a particular task. A researcher believed that reaction time could be reduced by using a motivating set of directions. For example, "If you can respond to this light in less than a second and a half I'll give you a quarter". A group of children with cerebral palsy were located and they completed the reaction time task under the condition of a motivating set of directions. The reaction time for the 12 children are given below. Determine whether the treatment was successful. (14 points)
1.4, 1.8, 1.1, 1.3, 1.6, 0.8, 1.5, 2.0, 1.4, 1.9, 1.8, 1.3
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