Question
In: Statistics and Probability
Each of the following three datasets represent IQ Scores for three random samples of different sizes....
Each of the following three datasets represent IQ Scores for three random samples of different sizes. The population mean is 100 population standard deviation is 15. Compute the sample mean, median and standard deviation for each sample size:
10) Using the sample size of 30 above in problem eight, your child was tested and has an IQ Score of 140. Calculate Z-Scores to answer these questions:
a. If your child has an IQ Score of 75, what percentage of the population has a lower score?
b. What percentage of the population has a IQ Score between 70 and 130?
c. If your child has an IQ Score of 140, what percentage of the population has a higher score?
Solutions
Expert Solution
Solution:
Given that ,
= 100
= 15
A sample of size n = 30 is taken from this population.
Let
be the mean of sample.
The sampling distribution of the
is approximately normal with
Mean
=
= 100
SD
=
= 15 /
30
= 2.7386
a) Find P(
< 75 )
= P[(
-
)/
< (75 -
)/
]
= P[Z < (75 - 100 )/ 2.7386]
= P[Z < -9.13]
z
score = -9.13
b) Find P(70 <
< 130)
= P(
< 130) - P(
< 70)
= P[(
-
)/
< (130 - 100)/2.7386] - P[(
-
)/
< (70 - 100)/2.7386]
= P[Z < 10.95] - P[Z < -10.95]
z
score = 10.95,-10.95
c) Find
P(
> 140 )
= P[(
-
)/
> (140 -
)/
]
= P[ (
-
)/
> (140 - 100 )/02.7386 ]
= P[Z > 14.61 ]
= 1 - P[Z < 14.61 ]
z
score = 14.61
orchestra answered 1 year agoRelated Solutions
Each of the following three datasets represent IQ Scores for three random samples of different sizes....
Each of the following three datasets represent IQ Scores for
three random samples of different sizes. The population mean is 100
population standard deviation is 15. Compute the sample mean,
median and standard deviation for each sample size:
Sample Size 30 106 92 98 103 100 102 98 124 83 70 108 121 102 87
121 107 97 114 140 93 130 72 81 90 103 97 89 98 88 103
Each of the following three data sets represents the IQ scores of a random sample of...
Each of the following three data sets represents the IQ scores
of a random sample of adults. IQ scores are known to have a mean
and median of 100. For each data set, determine the sample
standard deviation. Then recompute the sample standard deviation
assuming that the individual whose IQ is
108 is accidentally recorded as 180. For each sample size,
state what happens to the standard deviation. Comment on the role
that the number of observations plays in resistance....
Random samples of sizes
Random samples of sizes n1 = 25 and n2 = 20 were selected from populations A and B, respectively. From the samples, the standard deviations were computed to be s1 = 5.2 and s2 = 6.8.a. Do the data provide substantial evidence to indicate the populations have different standard deviations? Use α = .05.b. Estimate the relative sizes of the standard deviations by constructing a 95% confidence interval for the ratio of the standard deviations σ1/σ2.c. The data and populations...
Exercise 3 The data in the table represent the "Exam Scores" for two random samples of...
Exercise 3
The data in the table represent the "Exam Scores" for two random
samples of students. The first group of = 6 students were under
active-learning course, and the second group of = 6 students were
under traditional lecturing. Note that the standard deviations in
the Active group is = 3.43 and in the Traditional group is =
3.03.
Active learning
Traditional learning
0
7
5
0
7
8
8
2
0
4
3
3
Please answer the following...
Exercise 3 The data in the table represent the "Exam Scores" for two random samples of...
Exercise 3
The data in the table represent the "Exam Scores" for two random
samples of students. The first group of n1 = 6
students were under active-learning course, and the second group of
n2 = 6 students were under traditional lecturing.
Note that the standard deviations in the Active group is
s1= 3.43 and in the Traditional group is
s2 = 3.03.
Active learning
Traditional learning
0
7
5
0
7
8
8
2
0
4
3
3
Please...
The data below represent scores from three different therapies used to treat depressive symptoms. Scores represent...
The data below represent scores from three different therapies
used to treat depressive symptoms. Scores represent depressive
symptoms on a scale of 1-10, with higher scores indicating greater
depressive symptoms.
Treatment 1
Treatment 2
Treatment 3
0
1
4
0
4
3
G = 24
0
1
6
ΣX2 = 92
2
0
3
_______
T1 = 2
T2 = 6
T3 = 16
SS1 = 3
SS2 = 9
SS3 = 6
a. SST is what?
b. SSW is...
If two random samples, each with n = 60 scores, are selected from a population, and...
If two random samples, each with n = 60 scores, are selected
from a population, and the z-score and t statistic are computed for
each sample, the t statistics will be less variable than the
z-scores.
Two random samples are selected from two independent populations. A summary of the samples sizes, sample...
Two random samples are selected from two independent
populations. A summary of the samples sizes, sample means, and
sample standard deviations is given below:
n1=37,n2=44,x¯1=58.9,x¯2=74.7,s1=5.5s2=10.1 n 1 =37, x ¯ 1 =58.9, s
1 =5.5 n 2 =44, x ¯ 2 =74.7, s 2 =10.1 Find a 95.5% confidence
interval for the difference μ1−μ2 μ 1 − μ 2 of the means, assuming
equal population variances. Confidence Interval
Two random samples are selected from two independent populations. A summary of the samples sizes, sample...
Two random samples are selected from two independent
populations. A summary of the samples sizes, sample means, and
sample standard deviations is given below:
n1=39,n2=48,x¯1=52.5,x¯2=77.5,s1=5s2=11 Find a 97.5% confidence
interval for the difference μ1−μ2 of the means, assuming equal
population variances. Confidence Interval =
The following data represent the Intelligence Quotient Scores of a random sample of thirty adults. ...
The following data represent the Intelligence Quotient Scores of
a random sample of thirty adults. Construct a Stem-and-Leaf Plot
AND a Five Number Summary for the measurements. Compute the
locator of the median, the median, AND the mean of the thirty
measurements. Sample of Size n = 30 108 100 103 125 108 90 122 89
96 99 100 84 121 129 91 103 90 106 75 98 102 89 99 82 90 100 120
114 93 104
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- This is all one question, thank you so much in advance. The Bigbee Bottling Company is...
- For Questions 1-3: consider the following code: public class A { private int number; protected String...
- You are tasked with assessing the health department’s intervention program in preventing recurrence of acute alcohol...
- Compare the MOSFET, JFET , and BJT and identify the reasons these devices behave differently. What...
- How would you use SAS Enterprise Miner to create a neural network model of your example?
- Explain the use of neural networking modeling in predictive analytics.
- Current Market Mix of Netflix, as detail as possible, please.
ADVERTISEMENT