Question

A random sample is selected form a normal population with a mean of μ = 40 and a standard deviation of σ = 10. After a treatment is administered to the individuals in the sample, the sample mean is found to be M = 46.

a. How large a sample is necessary for this sample mean to be statistically significant? (Assume a two-tailed test with α = 0.05)

b. If the sample mean were M = 43, what sample size is needed to be significant for a two-tailed test with α = 0.05?

Answer #1

(a) For the sample mean of M = 46 to be statistically significant, the margin of error need to be atmost M - = 6 for 95% confidence interval

Let n be the sample size for margin of error to be 6

Critical z value corresponding to 95% CI (or two-tailed test with = 0.05) is 1.96

Thus, ≤ 6

-> ≤ 6

-> n ≥ 10.67

Thus, a sample of atleast 11 is necessary for the sample mean to be statistically significant

(b)

Similar to (a), here the margin of error needs to be atmost 43 - 40 = 3

Thus, ≤ 3

-> n ≥ 42.68

Thus, a sample of atleast 43 is necessary for the sample mean to be statistically significant

A random sample is selected from a normal popula-tion with a
mean of μ = 40 and a standard deviation of σ = 10. After a
treatment is administered to the individuals in the sample, the
sample mean is found to be M = 46.
How large a sample is necessary for this sample mean to be
statistically significant? Assume a two-tailed test with alpha =
.05.

A random sample is selected from a normal population
with a mean of μ=50 and a standard deviation of σ=12. After a
treatment is administered to the individuals in the sample, the
sample mean is found to be M=55.
a. If the sample consists of n=16 scores, is the sample
mean sufficient to conclude that the treatment has a significant
effect? Use a two-tailed test with α =0.05. b. If the sample
consists of n=36 scores, is the sample mean...

A
random sample is selected from a normal population with a mean of μ
= 20 and a standard deviation of σ =5 10. After a treatment is
administered to the individuals in the sample, the sample mean is
found to be M = 25. If the sample consists of n = 25 scores, is the
sample mean sufficient to conclude that the treatment has a
significant effect? Use a two-tailed test with alpha =
.05.

A sample of n = 16 individuals is randomly selected
from a population with a mean of μ = 65, and a treatment
is administered to the individuals in the sample. After treatment,
the sample mean is found to be M = 73.
(a) If the sample standard deviation is s = 11, are the
data sufficient to conclude that the treatment has a significant
effect using a two-tailed test with α = 0.05? (Round your
answers to three decimal...

A sample is randomly selected from a population with a mean of μ
= 50, and a treatment is administered to the individuals in the
sample. After treatment, the sample is found to have a mean of M =
56 with a standard deviation of s = 8. If there are n = 4
individuals in the sample, are the data sufficient to reject Ho and
conclude that the treatment has a significant effect using a
two-tailed test with =...

A sample of n=9 individuals is selected from a population with a
mean of μ=10. A researcher suspects that after the individuals have
gone through a specific type of treatment, their performances on a
standardized examination will be different from the general
population. After the treatment, the sample has a M=13 and
s2=9.
1. Using symbols, state the hypothesis for a two-tailed
test.
2. Calculate the t statistic and place this on a standardized
normal distribution.
3. With a two-tail...

A sample of n=18 individuals is selected from a population with
a mean of µ=77, and a treatment is administered to the individuals
in the sample. A treatment is administered to the individuals in
the sample and after treatment, the sample variance is found to be
s2=144.
a. If the treatment has a 3-point effect and produces a sample mean
of M=80, is this sufficient to conclude that there is a significant
treatment effect effect using a two-tailed test with...

A random
sample is selected from a normal population with a mean of µ = 30
and a standard deviation of σ= 8. After a treatment is administered
to the individuals in the sample, the sample mean is found to be x̅
=33.
Furthermore,
if the sample consists of n = 64 scores, is the sample
mean sufficient to conclude that the treatment has a significant
effect? Use a two-tailed test with α = .05.
4a. Which of
the following...

A treatment is administered to a sample selected from a
population with a mean of μ=40 and a variance of σ2=36.
After treatment, the sample mean is M=45. Based on this
information, calculate Cohen’s d and state the effect size.

A normal population has a mean of µ = 100. A sample of n = 36
is selected from the population, and a treatment is administered to
the sample. After treatment, the sample mean is computed to be
M = 106. Assuming that the population standard deviation
is σ = 12, use the data to test whether or not the treatment has a
significant effect. Use a one tailed test.
Hypothesis:
Zcrit =
z test
calculation:
Conclusion:

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 8 minutes ago

asked 17 minutes ago

asked 28 minutes ago

asked 29 minutes ago

asked 40 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago