Answer To: 1) 1 Question 1) The following table summarizes the weight (pound) of a sample of 100 adults...
Suraj answered on Jun 25 2021
1)
1
Question 1) The following table summarizes the weight (pound) of a sample of 100 adults patients admitted to one clinic. Each part 3 points total 15 points
Class interval
Number of patients
Class
Midpoint
Relative frequency
Cumulative frequency
Cumulative relative frequency
120—129
5
124.5
.05
5
.05
130—139
8
134.5
.08
13
.13
140—149
12
144.5
.12
25
.25
150—159
20
154.5
.2
45
.45
160—169
25
164.5
.25
70
.70
170—179
13
174.5
.13
83
.83
180—189
17
184.5
.17
100
1
Total
100
a) What proportion of the number of patients was admitted between 140 and 149?
1. .25
2. .2
3. .05
4. .12
Solution: The proportion is taken from the relative frequency column. Thus, between 140 and 149 the proportion of patients were 0.12. Thus, option (4) is correct.
b) What proportion of the number of patients was admitted between 140 and 169?
1. .25
2. .12
3. .57
4. .20
Solution: This proportion is taken from the cumulative relative frequency column. Thus, between 140 and 169 the proportion of patients were 0.7 – 0.13 = 0.57. Thus, option (3) is correct.
c) What class is the highest relative frequency?
1. 120-129
2. 140-149
3. 150-159
4. 160-169
Solution: The highest relative frequency is corresponding to highest frequency column and it is 160 – 169. Thus, option (4) is correct.
d) What class is the lowest frequency in the table?
1. 120-129
2. 140-149
3. 150-159
4. 160-169
Solution: The lowest relative frequency is corresponding to lowest frequency column and it is 120 – 129. Thus, option (1) is correct.
e) What type of graph would you use to present this data (you may have more than one type of graph)?
1. Histogram
2. Bar Graph
3. Pie Graph
4. All of above
Solution: The best way to present this kind of data is by the Histogram. Because histogram works better in grouped data. Thus, option (1) is correct.
Question 2) The following data is the information for weight loss of 20 patients going through program to lose weight. Each parts 2 points total 20 points
10,12,19,12,14,15,13,17,19,12,7,10,14,12,8,6,9,10,8,7
X=234 X 2=3016
You can use the following output below or calculate by hand to answers the questions:
Moments
N
20
Sum Weights
20
Mean
11.7
Sum Observations
234
Std Deviation
3.82650039
Variance
14.6421053
Skewness
0.48108759
Kurtosis
-0.4626092
Uncorrected SS
3016
Corrected SS
278.2
Coeff Variation
32.7051316
Std Error Mean
0.8556315
Basic Statistical Measures
Location
Variability
Mean
11.70000
Std Deviation
3.82650
Median
12.00000
Variance
14.64211
Mode
12.00000
Range
13.00000
Interquartile Range
5.50000
Tests for Location: Mu0=0
Test
Statistic
p Value
Student's t
t
13.67411
Pr > |t|
<.0001
Sign
M
10
Pr >= |M|
<.0001
Signed Rank
S
105
Pr >= |S|
<.0001
Quantiles (Definition 5)
Quantile
Estimate
100% Max
19.0
99%
19.0
95%
19.0
90%
18.0
75% Q3
14.0
50% Median
12.0
25% Q1
8.5
10%
7.0
5%
6.5
1%
6.0
0% Min
6.0
a) What is the mean?
1. 11.7
2. 12
3. 14.4
4. 15.5
Solution: From the Basic statistics measures table, the mean is 11.7. Thus, (1) is correct option.
b) What is the median?
1. 11.7
2. 12
3. 14.4
4. 15.5
Solution: From the Basic statistics measures table, the median is 12. Thus, (2) is correct option.
c) What is the mode?
1. 8
2. 10
3. 12
4. 19
Solution: From the Basic statistics measures table, the mode is 12. Thus, (3) is correct option.
d) What is range?
1. 11
2. 12
3. 13
4. 15
Solution: From the Basic statistics measures table, the range is 13. Thus, (3) is correct option.
e) What is variance?
1. 11.33
2. 10.89
3. 12.20
4. 14.64
Solution: From the Basic statistics measures table, the variance is 14.64. Thus, (4) is correct option.
f) What is standard deviation?
1. 3.83
2. 3.30
3. 3.49
4. 3.36
Solution: From the Basic statistics measures table, the standard deviation is 3.83. Thus, (1) is correct option.
g) What is the 25%?
1. 8
2. 9
3. 8.5
4. 9.5
Solution: The meaning of 25% is the first quartile i.e. Q1. Thus, 8.5 is the value of Q1. Hence, (3) is correct option.
h) What is the 75%?
1. 12
2. 14
3. 17
4. 19
Solution: The meaning of 75% is the third quartile i.e. Q3. Thus, 14 is the value of Q3. Hence, (2) is correct option.
i) What is interquartile range?
1. 3.5
2. 5.5
3. 2.5
4. 1.5
Solution: Interquartile defined as the difference between Q3 and Q1. Thus, 14 – 8.5 = 5.5. hence, (2) option is correct one.
j) What do you need to draw a box-and-whisker plot?
1. Min and max
2. Min , 25%,50%,75%, and max
3. 25%, 50%, and 75%
4. Variance and range
Solution: For a box plot, we need five measures. Those are minimum, Q1, median, Q3 and maximum. Thus, (2) is correct option.
Question 3) The following table is the results of survey for 1000 students asked if they smoked ever by gender. Four hundred of these were female and six hundred were male. ( each part 3 point , total 15 points)
Gender
Smoking
Smoked
Never Smoked
Male
200
400
Female
100
300
Total
300
700
a. Suppose we pick a student in random from this sample. What is the probability that this student ever smoked?
1. .4
2. .2
3. .1
4. .3
Solution: Probability that student smoked. Hence, option (4) is correct.
b. What is the probability of a student who male and never smoked?
1. .4
2. .2
3. .1
4. .3
Solution: Probability that student male and never smoked. Hence, option (1) is correct.
c. What is the probability of a student ever smoked given it was female?
1. .45
2. .25
3. .15
4. .35
Solution: Probability that student smoked given it was female. Hence, option (2) is correct.
d. Suppose we pick a student at random. What is the probability that student has ever smoked or being female or both?
1. .4
2. .2
3. .6
4. .3
Solution: Probability that student smoked or being female. Hence, option (3) is correct.
e. How many marginal probabilities do we have for this table?
1. Four
2. Eight
3. Six
4. None of above
Solution: Since, there are four factors in the table. Thus, four marginal probabilities table are there.
Question 4) Let say a medical research team examine a screening test for breast cancer. The following is the
Data of test by breast cancer status: ( each part 3 point , total 12 points)
Test result
Breast Cancer
Yes
No
Positive
45
10
Negative
5
440
Total
50
450
a) What is the sensitivity of test?
1. .90
2. .20
3. .02
4. .98
Solution: Sensitivity = . Hence option (1) is correct.
b) What is the specificity of test?
1. .90
2. .20
3. .02
4. .98
Solution: Specificity . Hence option (4) is correct.
c) What is the false negative and false positive?
1. .10 and .02
2. .15 and .25
3. .25 and .06
4. .15 and .15
Solution: False negative = 0.1 and false positive = 0.02. hence, option (1) is correct.
d) What is the positive predictive value and negative predictive value?
1. .88 and .90
2. .12 and .88
3. .18 and .12
4. .82 and .99
Solution: Positive predictive value = 0.82 and negative predictive value = 0.99. Hence option (4) is correct.
Question 5) Let say the percentage nursing student fail NCLCEX exam is 10. Suppose we take a simple random sample of 15 students. Find the probability that the number of students who fails NCLEX in the sample would be: Each parts 3 points total 9 points
a) One
1. .20
2. .34
3. .54
4. .11
Solution: Number of students failed = 1
. Hence, option (2) is correct.
b) What is the mean of the number of fail in NCLEX in sample size of 15?
1. 2
2. 1.5
3. 1
4. 3
Solution: Mean = 15*0.1 = 1.5. Hence, option (2) is correct.
c) What is the variance of the number of fail in NCLEX in sample size of...