Question

You are conducting an experiment in which you measure two means. Your null hypothesis is that they are the same (i.e. μ1 - μ2 = 0) and your experiment will test this hypothesis with a confidence level of alpha = 0.05. You would like to be able to detect a difference in means of+/- 1 with a probability of at least 0.9. How many samples do you need to test? The standard deviations of the two groups are σ1 = σ2 = 2.

Answer #1

The owner of two stores tracks the times for customer service in
seconds. She thinks store 1 has longer service times. Perform a
hypothesis test on the difference of the means. We know the
population standard deviations. (This is rare.)
Population 1 has standard deviation σ1=σ1= 4.5
Population 2 has standard deviation σ2=σ2= 4.5
The populations are normal. Use alph=0.05alph=0.05
Use the claim for the alternate hypothesis.
Service time store 1
174
184
170
174
174
189
174
179
176...

In order to compare the means of two populations, independent
random samples of 282 observations are selected from each
population, with the following results:
Sample 1
Sample 2
x¯1=3
x¯2=4
s1=110
s2=200
(a) Use a 97 % confidence interval to
estimate the difference between the population means
(?1−?2)(μ1−μ2).
_____ ≤(μ1−μ2)≤ ______
(b) Test the null hypothesis: H0:(μ1−μ2)=0
versus the alternative hypothesis: Ha:(μ1−μ2)≠0. Using ?=0.03, give
the following:
(i) the test statistic z=
(ii) the positive critical z
score
(iii) the negative critical z
score
The...

In the journal Mental Retardation, an article reported
the results of a peer tutoring program to help mildly mentally
retarded children learn to read. In the experiment, the mildly
retarded children were randomly divided into two groups: the
experimental group received peer tutoring along with regular
instruction, and the control group received regular instruction
with no peer tutoring. There were n1 =
n2 = 30 children in each group. The
Gates-MacGintie Reading Test was given to both groups before
instruction...

A random sample of
n1 = 49
measurements from a population with population standard
deviation
σ1 = 5
had a sample mean of
x1 = 8.
An independent random sample of
n2 = 64
measurements from a second population with population standard
deviation
σ2 = 6
had a sample mean of
x2 = 11.
Test the claim that the population means are different. Use
level of significance 0.01.(a) Check Requirements: What
distribution does the sample test statistic follow? Explain.
The...

A random sample of
n1 = 49
measurements from a population with population standard
deviation
σ1 = 3
had a sample mean of
x1 = 13.
An independent random sample of
n2 = 64
measurements from a second population with population standard
deviation
σ2 = 4
had a sample mean of
x2 = 15.
Test the claim that the population means are different. Use
level of significance 0.01.
(a) Check Requirements: What distribution does the sample test
statistic follow? Explain....

In the journal Mental Retardation, an article reported the
results of a peer tutoring program to help mildly mentally retarded
children learn to read. In the experiment, the mildly retarded
children were randomly divided into two groups: the experimental
group received peer tutoring along with regular instruction, and
the control group received regular instruction with no peer
tutoring. There were n1 = n2 = 36 children in each group. The
Gates-MacGintie Reading Test was given to both groups before
instruction...

It is desired to determine whether there is less variability in
the silver plating done by Company 1 than in that done by Company
2. If independent random samples of size 12 of the two companies’
work yield standard deviations s1 = 0.035 mil and s2 = 0.062 mil
respectively, test the null hypothesis that there is no difference
in variances (σ1^2 = σ2^2) against the alternative hypothesis that
variance of company 1 is smaller as compared to variance of...

You are conducting your own Rutherford scattering experiment in
lab by scattering 5.5 MeV α-particles off of gold foil. You
detector can detect a maximum of 2000 particles/sec. If you want to
design your experiment such that you detect at least 1 particle/sec
at a scattering angle of 50°, will you be able to use the same
detector to measure the count rate at a scattering angle of 6°?

A Michigan study concerning preference for outdoor activities
used a questionnaire with a six-point Likert-type response in which
1 designated "not important" and 6 designated "extremely
important." A random sample of n1 = 43 adults were asked about
fishing as an outdoor activity. The mean response was x1 = 4.9.
Another random sample of n2 = 48 adults were asked about camping as
an outdoor activity. For this group, the mean response was x2 =
5.6. From previous studies, it...

1) Two professors compare their commute times
to work. The first professor takes a random sample of 25 days and
finds an average commute time of 13.4 minutes and a standard
deviation of 55 seconds. The second professor takes a random sample
of 20 days and finds an average commute time of 19.6 minutes and a
standard deviation of 40 seconds At the .1 significance level,
conduct a full and appropriate hypothesis test for the professors
to see if the...

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