Answer Happy

An amusement park in a city would like to study whether
its number of visitors in Halloween can be used to predict its
number of visitors in Christmas. The data (in thousands of
visitors) over the past 14 years are shown in the table
below:
No. in Halloween
No. in Christmas
31.3
28.2
31.5
28.6
28.3
30.1
41.4
25.0
43.4
25.3
37.3
25.5
37.9
26.3
37.1
26.5
31.4
27.9
40.7
25.3
39.6
26.4
32.1
27.5
40.7
27.3
35.3
27.3
(a) Find the least-squares regression line from the
given data and interpret the slope.
Let X be the (answer) Christmas/ number of visitors
(in thousand) in Halloween/Halloween / number of visitors (in
thousand) in Christmas and
Y be the (Answer ) Christmas/ number of visitors (in
thousand) in Halloween / Halloween/ number of visitors (in
thousand) in Christmas.
The regression line is (Answer ) Y=a+bX / Y=ab/X/
Y=aX/b/ Y=ab+X/ Y=a+b/X/ Y=a/b+X where
the (answer) slope / y-intercept/
x-intercept a = _____ and
the (Answer) x-intercept/ slope/ y-intercept b
= ______ [correct to 4 decimal places].
The slope tells us that if the (Answer )Halloween/
number of visitors in Halloween / number of visitors in Christmas/
Christmas increases by 1 thousand, the (Answer )
number of visitors in Christmas/ number of visitors in Halloween/
Christmas/ Halloween will change
by _____ thousand (Answer ) on average/
by chance/ for sure.
(b) If the number of visitors in Halloween this year is
27.2 thousand, estimate the number of visitors this Christmas.
Also, comment on the validity of your prediction.
The regression line estimates that the number of visitors this
Christmas will be _____ thousand.
This prediction (answer) may not be valid / is
valid because the number _____ thousand
is (Answer)inside/outside the range of
observed (Answer)a/ X/Y/b/ r in the data.
(c) Determine and interpret the coefficient of
correlation.
The coefficient of correlation = _______.
It indicates a ( Answer
)moderate/strong/weak (Answer ) negative/ positive
(Answer ) curvilinear/ linear/ quadratic relationship of
the two variables.
(d) Determine and interpret the coefficient of
determination.
The coefficient of determination = _____
It implies that ________% of the variation in
the (Answer) number of visitors in Christmas/ Halloween/
number of visitors in Halloween/ Christmas can be explained by
the variation in the ( Answer ) Halloween/ number
of visitors in Halloween/ number of visitors in Christmas/
Christmas to the amusement park.
(e) At the 0.01 level of significance, is there evidence
of a linear relationship between the number of visitors in
Halloween and the number of visitors in Christmas to the amusement
park?
The (Answer) alternative/ true/ false/ null hypothesis
H0 is:
The (Answer)
population/sample correlation coefficient 𝜌 (answer)
>/ =/ NOT=/ </ >=/ <=/ ______.
The (Answer) alternative/ true/ false/ null hypothesis H1
is
The (Answer)
population/sample correlation coefficient 𝜌 (answer)
>/ =/ NOT=/ </ >=/ <=/ ______.
The (Answer) power of the test/ level of significance/
level of confidence 𝛼 = ______ [give a value between
0 and 1 correct to 4 decimal places].
The (Answer) population size / sample size/ sampling
rate 𝑛 = _______
The chosen test statistic is:
𝑡=(𝑋¯−𝜇)/(𝑆/𝑛√)
𝑡=(𝑟−𝜌)/(1−𝑟2)/(𝑛−2)
𝜒2=∑(𝑓𝑜−𝑓𝑒)2/𝑓
𝑍=(𝑋¯−𝜇)/(𝜎/𝑛√)
𝑍=(𝑝−𝜋)/𝜋(1−𝜋)/𝑛
and the test should be a (Answer)upper-tail/ lower-tail/
two-tail test.
The critical value is ______ [give a positive value
correct to 4 decimal places].
The decision rule is then:
Reject (Answer)
H1/H0 if (Answer) test statistic NOT= critical value/
-critical value < test statistic < critical value / test
statistic < -critical value / test statistic = critical value OR
test statistic = -critical value / test statistic > critical
value / test statistic > critical value OR test statistic <
-critical value/ test statistic = critical value;
Do not reject (Answer)
H0/H1 otherwise.
From the given data, the test statistic is found to
be _____ [correct to 4 decimal places].
Hence, (Answer) H0 is rejected/ H0 is not rejected/ H1 is
rejected/ H1 is not rejected and there is (Answer)
sufficient/ insufficient evidence of a (Answer)quadratic/
linear/ curvilinear relationship between the number of
visitors in Halloween and the number of visitors in Christmas to
the amusement park at the 0.01 level of significance.