Question
In: Statistics and Probability
A sample of n=25 scores is selected from a normal population with μ = 100 and...
A sample of n=25 scores is selected from a normal population with μ = 100 and σ = 20 .
a. What is the probability that the sample mean will be greater than 120?
b. What is the probability that the sample mean will be less than 105?
c. What is the p (90 < M < 110)?
Solutions
Expert Solution
z score for normal distribution formula
z = (M - μ) / (σ / sqrt(n))
a. What is the probability that the sample mean will be greater than 120?
z = (120 - 100) / (20/sqrt(25)) = 5
P(Z > 5) = 0
The probability that the sample mean will be greater than 120 = 0
b. What is the probability that the sample mean will be less than 105?
z = (105 - 100) / (20/sqrt(25)) =1
P(Z < 1) = 0.8413
c. What is the p (90 < M < 110)?
z = (90 - 100) / (20/sqrt(25)) = -3
z = (110 - 100) / (20/sqrt(25)) = 3
p (90 < M < 110) = 0.9973
orchestra answered 2 years agoRelated Solutions
A random sample of n = 100 scores is selected from a normal population with a...
A random sample of n = 100 scores is selected from a normal
population with a mean of μ = 60 and a standard deviation of σ =
20. What is the probability of obtaining a sample mean greater than
M = 57?
A random sample of n =100 is selected from a normal population with mean μ =...
A random sample of n =100 is selected from a normal
population with mean μ = 24 and standard deviation
σ = 1.25.
Find the probability that is less than 24.3
A sample of n = 4 individuals is selected from a normal population with μ = 70 and σ = 10.
3) A sample of n = 4 individuals is selected from a normal population with μ = 70 and σ = 10. A treatment is administered to the individuals in the sample, and after the treatment, the sample mean is found to be 75.
a) On the basis of the sample data, can you conclude that the treatment has a significant effect?
(Use a two-tailed test with α = .05).
b) Suppose that the sample consisted...
If, in a sample of n=25 selected from a normal population, X=52 and S=10, what is...
If, in a sample of n=25 selected from a normal population,
X=52 and S=10, what is your statistical decision if the level of
significance, a, is 0.05 the null hypothesis, H0, is μ=50, and
the alternative hypothesis, H1, is μ≠50?
The population of IQ scores form a normal distribution with a μ = 100 and a...
The population of IQ scores form a normal distribution with a μ
= 100 and a standard deviation of σ = 10. What is the probability
of obtaining a sample mean greater than M = 97, For a random sample
of n = 9 For a random sample of n = 25 people
A random sample of n measurements was selected from a population with unknown mean μ and...
A random sample of n measurements was selected from a population
with unknown mean μ and standard deviation σ=35 for each of the
situations in parts a through d. Calculate a 95% confidence
interval for muμ
for each of these situations.
a. n=75, x overbarx=22
b. n=150,x overbarxequals=110
c. n=90, x overbarxequals=18
d. n=90,x overbarxequals=4.69
e. Is the assumption that the underlying population of
measurements is normally distributed necessary to ensure the
validity of the confidence intervals in parts a...
A random sample of n measurements was selected from a population with unknown mean μ and...
A random sample of n measurements was selected from a population
with unknown mean μ and standard deviation σ = 15 for each of the
situations in parts a through d. Calculate a 99% confidence
interval for μ for each of these situations.
a. n = 75, x̄ = 27
b. n = 150, x̄ = 105
c. n = 125, x̄ = 16
d. n = 125, x̄ = 5.37
e. Is the assumption that the underlying population of...
A sample of n = 9 scores is obtained from a normal population distribution with σ...
A sample of n = 9 scores is obtained from a normal
population distribution with σ = 12. The sample mean is M
= 60.
a. With a two-tailed test and α = .05, use the sample data to
test the hypothesis that the population mean is μ = 65.
b. With a two-tailed test and α = .05, use the sample data to
test the hypothesis that the population mean is μ = 55.
c. In parts (a) and...
A researcher selects a sample of n=25 individuals from a population with a mean of μ=60...
A researcher selects a sample of n=25 individuals from a
population with a mean of μ=60 and standard deviation of σ=10 and
administers a treatment. The researcher predicts that the treatment
will increase scores. Following the treatment, the average scores
for this sample is M=65.
1. Using symbols, state the hypothesis for a one-tailed
test.
2. Calculate the z-score and place this on a standardized normal
distribution.
3. With a one-tail α=0.05, state the conclusion of these
findings.
4. Calculate...
8. A sample of n = 4 individuals is selected from a normal population with m...
8. A sample of
n = 4 individuals is selected from a normal population
with m = 70 and s = 10. A treatment is administered to the
individuals in the sample, and after the treatment, the sample mean
is found to be M = 75.
A. On the basis of the sample data,
can you conclude that the treatment has a significant effect? Use a
two-tailed test with a = .05.
B. Suppose that the sample consisted
of n...
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- 3) You are rolling a 12 sided die 8 times. a) What is the size for...
- explain the difference between quantitative and qualitative research strategies. Provide an example of a crime based...
- use postorder and inorder tree traversals to make preorder traversal. #!/usr/bin/env python3 # encoding: UTF-8 """Turning...
- 1. Write an if-else statement to describe an object. Print "Balloon" if isBalloon is true and...
- An investor is considering purchasing a Treasury bond with a 20 year maturity, an 8% coupon...
- Write a program that copies the contents of one file to a destination file. This program...
- how to conduct a marketing mix for 3d crest white strips
ADVERTISEMENT