solution

What proportion of males and females have a slightly elevated heart rate that is between 81-90 beats per minute?

What is the dependent variable crime rate in that neighborhood

 

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Assignment-1

1.Which of the following is most likely to be a nominal variable?

a) Weight gain in first-year college students

b) Annual salary in a sample of nurses

c) Species of dogs appearing in the Sunday comics

d) Deterioration in driving performance under the influence of alcohol

e) Hours spent studying for a statistics exam

 

2.You want to know whether right-handed people have a dexterity advantage over left- handed people. You measure the amount of time it takes 10 people of each handedness group to open a child-proof container and calculate the average time taken for each group. If you were to graph these data, the type of graph you should use is a:

a) bar graph

b) histogram

c) line graph

d) pie chart

e) scatterplot

 

3.Which of the following is true:

a) Measures of central tendency include the mode, median and range

b) Descriptive statistics describe a set of data by indicating where the center of the distribution is and how tightly or loosely the data are spread about the center

c) Measures of dispersion include the range, variance and mode

d) The mode is the most useful measure of central tendency

e) Both A and C are true

 

4.Suppose a researcher in a health clinic for geriatric patients measures the heart rate of every patient that visits the clinic in a single day. The researcher creates the following histogram, separated for male and female patients.

histagram

What proportion of males and females have a slightly elevated heart rate that is between 81-90 beats per minute?

a) 20% of the males and 28% of the females

b) 20% of the males and 20% of the females

c) 20% of the males and 0% of the females

d) 26% of the males and 21% of the females

e) 7% of the males and 8% of the females

 

5.Looking at the Histogram above, do you see anything wrong? If so, what is it?

How would you choose to represent this data?

For questions 5-9 use the following data set:

1    5    7    4    3    9    2    6    1    7    5    4    3    9    2    11

 

6.What are the mode and median of the data set?

a) Mode is 3.5 and median is 4.5

b) Both mode and median are 7

c) There is no clear mode and median is 4.5

d) Mode is 1 and median is 16

e) There is no clear mode and median is 5

 

7.What is the mean of the data set?

a) 9

b) 4

c) 1

d) 5

e) 9

 

8.What is the range of the data set?

a) 1

b) 5

c) 10

d) 11

e) None of the above

 

9.In the above data set, assume that the person entering the data made a mistake and accidentally entered one of the values of 5 as 55. In such a case, which of the following descriptive statistics would be affected by this change?

a) Mode, range and variance

b) Median, mean and standard deviation

c) Mean, range and variance

d) Interquartile range, variance and standard deviation

e) Median, variance and standard deviation

 

10.In the situation described in Question 9, what would the graph likely look like?

a) Positively skewed

b) Negatively skewed

c) Normal

d) Symmetrical

e) Uniform

 

11.In Massachusetts, eight individuals experienced unexplained episode of vitamin D intoxication that required hospitalization; it was thought that these unusual occurrences might be the results of excessive supplementation of dairy milk. Blood levels of calcium and albumin-a type of protein for each subject at the time of hospitalization are provided below:

a) Find the mean, median, standard deviation, interquartile range and range of the recorded calcium levels.

b) Find the mean, median, standard deviation, interquartile and range of the albumin levels.

c) For healthy individuals, the normal range of calcium values is 2.12 to 2.74 mmol/l, while the range of the albumin levels is 32 to 55g/l. Do you believe that patients suffering from vitamin D intoxication have normal blood levels of calcium and albumin?

Calcium(mmol/l) Albumin(g/l)
2.92 43
3.84 42
2.37 42
2.99 40
2.67 42
3.17 38
3.74 34
3.44 42

 

Assignment-2

1.You give a comprehension test and you find that the student’s scores are normally distributed. The mean (µ) = 60. The standard deviation =10. There are 200 students in the class.

a.How many of your 200 students will have a score greater than 60?

b.A score of 70 is ___________ standard deviations ___________ the mean.

c.What percent of the class will have a score greater 70?

d.What percent of the class will have a score less than 70?

e.How many of your 200 students will have a grade greater than 70?

f.What percent of the class will have scores between 50 and 70?

g.Kyra’s score is 78. What percent of the class scored less than her?

h.Glen’s score is 46. What percent of the class had scores greater than him?

i.What percent of the scores lie between Kyra’s and Glens?

 

2.You are teaching a statistics class (though your students might think of it more sadistics). You decide that you are going to grade “on the normal cure”.  The following table is used to determine the student’s grades:

Grade Z-score
A above 1.5
B 0.5-1.5
C -0.5 to 0.5
D -1.5 to -0.5
F Below-1.5

 

Using this system, what percent of As Bs, Cs Ds and Fs are expected with a normal distribution of scores?

 

3.You are running a study to compare the cognitive capacity of children with DS to that of the “normal” population using the S-B IQ test. For the normal population, the test has a mean of 100 and a standard deviation of 15.  You randomly sample 100 children with DS and find that their IQ is 80.

a.state the null hypothesis

b.state the alternative hypothesis for a two-tailed test

c.state the alternative hypothesis for a one-tailed test

d.what is the standard error of the mean

e.What is the probability of getting a mean of 80 under the null hypothesis?

f.At the conventional a level of .05, can we reject the null hypothesis?

 

4.A sampling distribution:

a.has a dispersion less than that of the original distribution from which the samples were drawn.

b.has a dispersion greater than that of the original distribution from which the samples were drawn.

c.depicts multiple individual observations

d.depicts multiple sample means (from repetitive samplings) taken from the same population.

e.b and d are true

f.a and d are true.

 

5.Based on Central Limit theorem, we know that the sampling distribution of means taken from a uniform distribution will

a.be identical to that of the original population from which the samples were drawn.

b.approach a normal distribution

c.be negatively skewed

d.be positively skewed

 

6.For a confidence interval of 95%, the critical Z values are -1.96 and +1.96. You decide to use a confidence interval of 80%. What are the critical Z values?

 

Chose the one best answer.

1.Which of the following is true concerning the intervals of a histogram (class intervals)?

a.Each interval should be the same width

b.Class intervals should be non-­‐overlapping

c.Class intervals should be consecutive

d.All of the above

 

2.Which of the following is not true concerning histograms?

a.The class intervals of the variable are usually plotted on the x-­‐axis

b.The frequency of the each interval is usually plotted on the y-­‐axis

c.The vertical bars representing the frequency of each class interval are usually separated

d.Histograms graphically represent interval/ratio data

 

3. Which of the following measures of central tendency may be used with interval/ratio data?

a.Mode

b.Median

c.Mean

d.All of the above

 

4.Fill in the approximate percentages on the normal distribution shown below.

a.2.1

b.13.6

c.34.1

d.34.1

e.13.6

f.2.1

 

5.The level of significance specifies the probability of committing a error.

a.Non-­-

b.β

c.Type I

d.Type II

 

6.Which of the following is the correct general statement of a directional (one-­‐tailed) alternative hypothesis for the one-­‐sample hypothesis test when a researcher predicts a decrease?

a.µ = a

b.µ ≠ a

c. µ > a

d. µ < a

 

7.If t(obs) = -­‐2.03 and t(critical) = +1.753, what decision would you make concerning the null hypothesis?

a.Reject

b.Fail to reject

c.That you probably made a Type I error

d. That you probably made a Type II error

 

8.If you have 15 subjects in each of the two independent samples, how many degrees of freedom do you have?

a.13

b.28

c.29

d.30

 

9.If degrees of freedom for a dependent-­‐samples test equal 9, how many pairs of scores were in the original set of data?

a.8

b.10

c.18

d.20

 

10.Which of the following is a prerequisite for conducting a dependent-­‐samples t test?

a.The samples must be related to one another

b.There must be two scores for each subject (or related subjects)

c.The pairs of data must be kept in the same order for each subject (or each pair of related subjects)

d.All of the above

 

11.Multiple t-­‐tests have an inflated probability of a error.

 

12.The F-­‐ratio in a one-­‐way ANOVA is the ratio of the group variance and the group variance.

 

13.A mean square is a sum of square divided by its associated .

 

14.If the null hypothesis is true, F will be

a.much less than 1

b. close to 1

c.much greater than 1

d. close to 0

 

15.If MS(between) = 13 and MS(within) = 2, then F =

a.6.5

b. 0.15

c.   1

d.Not enough information provided

 

16.If the sample size, the power will

a.decreases, increase

b. increases, decrease

c.  decreases, decrease

d.  increases, increase

e.  both a and b

f.both c and d

 

17.Suppose that you are conducting a preference test among three brands of children’s cereal. What would the expected value for each category be among a sample of 60 children if there was no preference expected?

a.6

b.10

c.20

d.30

 

18.The appropriate test to determine the relationship between two variables measured at the nominal level of measurement is

a.Pearson’s r

b.Chi-­‐Square Goodness of Fit

c.Chi-­‐Square test of independence

d. ANOVA’

 

19.What test is most appropriate?

1)   Suppose you are interested in convincing high school students to avoid taking drugs, and you prepare three films to be shown to the students. You wish to know

whether there is any difference in the films’ effectiveness in persuading students to avoid drugs. You select a group of 60 students, 30 males and 30 females, and randomly assign each to one of three groups. Each group will then see one of the films, and students will rate themselves on the drug attitude scale. Previous research has shown that a film might differently affect males than females.

 

20.If the null hypothesis is Ho: u=69 and a confidence interval ranges from 50 to 58, what decision would you make concerning the null hypothesis?

a.Reject

b.Fail to reject

c.That you had probably made a Type I error

d. That you had probably made a Type II error

 

21.When determining the 95% confidence interval for a sample mean, the value of the critical value of t is equal to

a.1.645

b. 1.96

c.2.58

d.it depends on the degrees of freedom

 

22.Suppose you want to know whether crowding in a neighborhood is related to the crime rate in that neighborhood. You rate the city’s neighborhoods according to the room occupancy rate (the number of occupants in a dwelling divided by the number of rooms in that dwelling) and the number of times police were summoned to that neighborhood in the past year. In this study:

a.what is the independent variable Tha neighborhood]

b.what is the dependent variable crime rate in that neighborhood

c.what is the best way to visually present this data sctler graph

 

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