Question

T test results- t-statistic, df, p-value. What the output means, both statistically and in terms of differences between the sites?

t(5) = -5.11, p=0.0037

Anova results- F-statistic, df (between and within groups), p-value. What the output means, both statistically and in terms of differences between the sites?

F(5, 36) = 4.26, p=0.0038

Linear Regression results-F-statistic, df (regression and residual), p-value, R2. What the output means, both statistically and in terms of differences between the sites?

F(1,91)=794, p=0.011, R2=0.90

Answer #1

(A) t(5) = -5.11, p=0.0037

p value(0.0037) is less than significance level 0.05, we will reject the null hypothesis because result is statistically significant.

This means that there is sufficient evidence to conclude that the means differ significantly.

(B) F(5, 36) = 4.26, p=0.0038

p value(0.0038) is less than significance level 0.05, we will reject the null hypothesis because result is statistically significant.

This means that there is sufficient evidence to conclude that at least two means differ significantly.

(C) F(1,91)=794, p=0.011, R2=0.90

p value(0.011) is less than significance level 0.05, we will reject the null hypothesis because result is statistically significant.

This means that there is sufficient evidence to conclude that at least two means differ significantly.

R^2 is 0.90, which means that 90% of variation in dependent variable is explained by the model.

Suppose you conduct an ANOVA test and determine an F statistic
of 2.14 with a p-value of 0.21. You should ____________.
a.
conduct a Tukey-Kramer procedure to further evaluate differences
between the means being tested
b.
conclude that none of the means being tested are equal to one
another
c.
conclude that there is not evidence of differences between the
population means being tested
d.
conclude that there is at least one difference between the means
being tested

The t-test paired scores go like that:
t = 8.812, df = 46, p-value = 0.00000000001936
CI (95%): 3.677283 & 5.854632
The mean of the differences: 4.765957
Decide whether statements below are true and explain why:
1) Classical hypothesis testing would recognize a significant
difference here
2) Because the estimates of means are different, with 95% there is
a difference between the means in the (imaginary) population,
3)The confidence interval includes 0, so it’s possible that
there is no real...

The One-Way ANOVA applet lets you see how the
F statistic and the P-value depend on the
variability of the data within groups, the sample size, and the
differences among the means.
(a)
The black dots are at the means of the three groups. Move these
up and down until you get a configuration that gives a
P-value of about 0.01. What is the value of the F
statistic?
_______________________________________________________________________________________________________________________________________________________
(b)
Now increase the variation within the groups by sliding...

7) Identify and interpret the adjusted R2 (one paragraph):
What does the value of the adjusted R2 reveal about the
model?
If the adjusted R2 is low, how has the choice of independent
variables created this result?
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.60
R Square
0.36
Adjusted R Square
0.26
Standard Error
9.25
Observations
30.00
ANOVA
df
SS
MS
F
Significance F
Regression
4.00
1212.46
303.12
3.54
0.02
Residual
25.00
2139.14
85.57
Total
29.00
3351.60
Coefficients
Standard Error
t...

Identify and interpret the F test (one paragraph):
Using the p-value approach, is the null hypothesis for the F
test rejected or not rejected? Why or why not?
Interpret the implications of these findings for the
model.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.60
R Square
0.36
Adjusted R Square
0.26
Standard Error
9.25
Observations
30.00
ANOVA
df
SS
MS
F
Significance F
Regression
4.00
1212.46
303.12
3.54
0.02
Residual
25.00
2139.14
85.57
Total
29.00
3351.60
Coefficients
Standard Error
t...

Use the multiple regression output shown to answer the following
questions.
The regression equation is
Y=9.40+0.332X1+0.067X2-0.251X3
Predictor
Coef
SE Coef
T
P
Constant
9.395
6.858
1.37
0.184
X1
0.3316
0.8962
0.37
0.716
X2
0.0666
-0.0520
-1.28
0.214
X3
-0.2508
-0.1036
2.42
0.025
S=4.84768
R-Sq=15.0%
R-Sq(adj)=2.8%
Analysis of Variance
Source
DF
SS
MS
F
P
Regression
3
86.8
28.93
1.23
0.322
Residual Error
21
493.5
23.5
Total
24
580.3
a) Which variable might we try eliminating first to possibly
improve this...

In an experiment designed to test the output levels of three
different treatments, the following results were obtained: SST =
320, SSTR = 130,
nT = 19.
Set up the ANOVA table. (Round your values for MSE and
F to two decimal places, and your p-value to four
decimal places.)
Source
of Variation
Sum
of Squares
Degrees
of Freedom
Mean
Square
F
p-value
Treatments
Error
Total
Test for any significant difference between the mean output
levels of the three treatments....

The following table is the output of simple linear regression
analysis. Note that in the lower right hand corner of the output we
give (in parentheses) the number of observations, n, used
to perform the regression analysis and the t statistic for
testing H0: β1 = 0 versus
Ha: β1 ≠ 0.
ANOVA
df
SS
MS
F
Significance F
Regression
1
61,091.6455
61,091.6455
.69
.4259
Residual
10
886,599.2711
88,659.9271
Total
11
947,690.9167
(n = 12;...

Run the test in SPSS.
What was the t-statistic?
6.702 [1 point]
What were the confidence intervals? .25,
.47 [1 point]
What was the p-value? 0 [1
point]
PASTE YOUR SPSS OUTPUT HERE! [2 points]
One-Sample
Test
Test Value = 0
t
df
Sig. (2-tailed)
Mean Difference
95% Confidence
Interval of the Difference
Lower
Upper
What is your
gender?
6.702
79
.000
.363
.25
.47
1. Write up your results in APA
format. Your write-up should include sample mean(s)/standard
deviation(s),...

T F 1. A p-value of .008 in hypothesis testing means there is
only a .8% chance we could get such sample statistics from the
population if the null hypothesis is as stated. Such an event is
considered unlikely and we would reject the null hypothesis.
T F 2. As a general rule in hypothesis testing, it is always
safer to set up your alternate hypothesis with a greater-than or
less-than orientation.
_____3. If the level of significance is .02...

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