Question

Paired sample t-test:

Suppose you are interested in deciding if a particular diet is effective in changing people's weight. You decide to run a "within subject" experiment. You select 6 people and weigh each of them. Two weeks and you weigh them again. For each person you compute how much weight they lose over this period. You find : Non-diet (subject 1-6): 0,8,3,2,-10,-1. You then put them on the diet and weigh them again after two weeks and compute how much they lose over this period. Diet: (subject 1-6): 1,6,4,3,-8,2.

a. compute the null and alternative hypotheses

b. compute the mean and standard deviation of the difference distribution

c. how many degrees of freedom?

d. assume the null hypothesis is true and compare the t-statistic

e. compute p-value

f. at an alpha =0.05 would you accept or reject null?

Suppose the research assistant lost the information that linked the subjects identity across the two weight loss periods. This makes it impossible to run a paired t-test. Rather than start over:

a. compute the mean and standard deviation

b. compute the two sample t-statistic

c. how many degrees of freedom?

d. compute p-value

e. how does this p-value compare to the one you just compared using the paired t-test?

Answer #1

Suppose you are interested in deciding if a particular diet is
effective in changing people's weight. You decide to run a "within
subject" experiment. You select 6 people and weigh each of them.
Two weeks and you weigh them again. For each person you compute how
much weight they lose over this period. You find : Non-diet
(subject 1-6): 0,8,3,2,-10,-1. You then put them on the diet and
weigh them again after two weeks and compute how much they lose...

Paired Samples t-test (30pts) Suppose you are interested in
deciding if a particular diet is effective in changing people’s
weight. You decide to run a “within subject” experiment. You select
6 people and weight each of them. Two weeks, you weight them again.
For each person you compute how much weight they lost over this
period. This is what you find: Non-diet(subject 1-6): 0 8 3 2 -10
-1 You then put them on the diet and weigh them again...

One-sample t:
Suppose you are a big fan of world cup soccer and want to know
if the soccer ball that is going to be used in the next world cup
is a different weight than the balls used in the last world
cup.
a. Would you formulate this as a one or two sided hypothesis
test?
Suppose the average weight of the ball used in the last world
cup was 500g.
b. State the null and alternative hypotheses for...

7.126 Two-sample t test versus matched pairs t test. Consider
the following data inspections are available through its online
newspaper. patrons at risk of getting sick and must immediately be
corrected by the restaurant. An SRS of n = 200 inspections from the
more than 16,000 inspections since January 2012 were collected,
resulting in x ̄=0.995 violations and s = 1.822 violations.
Critical food violations are those that put set. The data were
actually collected in pairs, and each row...

Then you will do a paired t-test on the two # of letters
variables using a level of significance. What is the test-statistic
and p-value?
# of letters in first name
#letters in last name
5
6
5
5
7
7
4
6
7
7
6
5
7
9
6
9
4
12
5
7
4
5
7
5

Assume that you want to test the claim that the paired sample
data come from a population for which the mean difference is
μd = 0. Compute the value of the t test statistic. Round
intermediate calculations to four decimal places as needed and
final answers to three decimal places as needed.
x
7
4
10
3
13
y
4
6
6
4
8
t = 0.415
t = 1.292
t = 2.890
t = 0.578

How do you determine whether or not the paired t test is
appropriate for a two-sample hypothesis? Please give an
example.

Suppose you take two random samples of dieters to show that
those on a Low-Carb Diet lose more weight than those on a Low-Fat
Diet. Use the following table to test the hypothesis H0:
µ1 ≤ µ2 versus H1: µ1
> µ2 at 0.10 level of significance (Assume that the
population variances are equal but unknown). Which of the following
statements is true?
weight loss(in pounds)
, low carb diet group 1 , low fat diet
group 2...

How do you determine whether or not the paired t test
is appropriate for a two-sample hypothesis? please provide numeric
example.

A diet center claims that it has the most effective weight loss
program in the region. Its advertisements say, “Participants in our
program lose more than 4 pounds within a month.” Six clients of
this program are weighed on the first day of the diet and then one
month later. Let the difference be defined as Weight on First Day
of Diet minus Weight One Month Later. (You may find it
useful to reference the appropriate table: z table
or...

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