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- From: Mathematics, Statistics and Probability
- Posted on: Sat 23 Jan, 2016
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1.
Identify each of the following as examples of nominal, ordinal, interval, or ratio scales of measurement.
A poll of registered voters in Florida asking which candidate they support Nominal
The length of time required for a wound to heal when using a new medicine Ratio
The number of telephone calls arriving at a switchboard per five-minute period Ratio
The distance first-year college football players can kick a ball Ratio
Mental health diagnoses present in an elderly population Nominal
The rankings of employees on their job performance Ordinal
2.
Two hundred raffle tickets are sold. Your friend has five people in her family who each bought two raffle tickets. What is the probability that someone from her family will win the raffle?
Probability = (5 * 2)/200 = 0.05
3. Jolie has 45 minutes to do her statistics homework. If the mean is 38 minutes and the standard deviation is 3, calculate Jolie's z score. Once calculated, interpret your findings in terms of Jolie's performance.
(HINT: use the normal distribution and the probability that other students performed better or worse.)
z = (x – ?)/? = (45 – 38)/3 = 2.33
P(x < 45) = P(z < 2.33) = 0.9902
If Jolie takes 45 minutes to do the work, she has taken 2.33 standard deviations more time than the average time required to complete the work. 99% of the students have completed the work before Jolie.
4. A psychologist measures units of change for a memory test after students are given an opportunity to sleep only four hours. The following change units were obtained: 7, -12, 4, -7, 3, -10. Find the a) mean, b) median, c) mode, d) standard deviation, e) range, and f) variance.
(a) -2.5 (b)-2 (c) No mode (d) 8.12 (e) 19 (f) 65.90
5. A student scored 81 on a chemistry test and 75 on a history test. For the chemistry test, the mean was 70 and the standard deviation was 20. For the history test, the mean was 65 and the standard deviation was 8. Did the student do better on the chemistry test or the history test? Explain your answer.
z- score for Chemistry test = (81 – 70)/20 = 0.55
z- score for History test = (75 – 65)/8 = 1.25
Student did better in History test since the z- score is positive and greater than that for Chemistry test
6. Suppose you want to figure out what to do with your degree in psychology. You ask some fellow students from your psychology program who recently graduated to find out what they are doing with their degree and how much it pays. What type of sampling is this? What are the limitations of this sampling approach?
This is convenience sampling because you are asking only a limited number of graduate students whom you know or whom you can catch hold of easily. The limitation is that since the sampling is not random, the results may not be reliable.
7. Variables in which the values are categories are known as
Interval variables
Nominal variables
Ordinal variables
Ratio variables
8. Before the researcher can conduct a statistical test, the research question must be translated into
A testable hypothesis
Additional observations
Mathematical symbols
Numbers
9. The hypothesis stating that there are no differences, effects, or relationships is
The alternative hypothesis
The baseline hypothesis
The null hypothesis
The reasonable hypothesis
10. A group of students made the following scores on a 10-item quiz in psychological statistics: {5, 6, 7, 7, 7, 8, 8, 9, 9, 10, 10} What is the mean score?
6.6
7.2
7.8
8.7
11. A group of students made the following scores on a 10-item quiz in psychological statistics: {5, 6, 7, 7, 7, 8, 8, 9, 9, 10, 10} What is the median score?
6
7
8
9
12. A group of students made the following scores on a 10-item quiz in psychological statistics: {5, 6, 7, 7, 7, 8, 8, 9, 9, 10, 10} What is the mode?
5
7
8
9
13. A group of students made the following scores on a 10-item quiz in psychological statistics: {5, 6, 7, 7, 7, 8, 8, 9, 9, 10, 10} What is the range of scores?
5
6
7
11
14. A group of students made the following scores on a 10-item quiz in psychological statistics: {5, 6, 7, 7, 7, 8, 8, 9, 9, 10, 10} What is the variance, treating these scores as a sample?
1.53
1.60
2.33
2.56
15. The standard normal distribution has all the following properties EXCEPT:
The mean, mode, and median are all equal
The total area under the curve equals 1
The curve is specified by two parameters, the mean and the standard deviation
The curve extends to + and – 3 standard deviations from the mean
16. According to the Empirical Rule, approximately _______% of the data in a normal distribution will fall within ±1 standard deviation of the mean. )
34
68
95
99.7
17. In statistical computations, the number of values that are free to vary is known as
Degrees of freedom
Freedom factor
Variability index
Variation quotient
18. Which of the following reflects a Type I error?
Rejecting the null hypothesis when in reality the null hypothesis is true
Rejecting the null hypothesis when in reality the null hypothesis is false
Accepting the null hypothesis when in reality the null hypothesis is true
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