Hypothesis Testing and Regression Analysis in Statistics

Statistics
Student Name:
Instructor Name:
Course Number:
26th April 2019

Task 1:
We computed the two random samples, each of size 200, with one sample taken from those
movies made before 2010 and the other sample taken from those movies made in 2010 - 2019,
using the formula RAND(). The results are presented in excel attached with this report.
TASK 2:
Using a 5% significance level, we sought to test the hypothesis that the proportion of movies
made in 2010 - 2019 with a runtime of at least 2 hours is significantly different from the
proportion of movies made before 2010 with a runtime of at least 2 hours.
The tested hypothesis is given as follows;
H0 : p1= p2
H A : p1 ≠ p2
Where p1= proportion of movies made before 2010 with a runtime of at least 2 hours
p2= proportion of movies made∈2010−2019 with a runtime of at least 2 hours
The results are presented below;
Results
Sample 1 Sample 2 Difference
Sample proportion 0.27 0.26 0.01
95% CI (asymptotic) 0.2085 - 0.3315 0.1992 - 0.3208 -0.0765 - 0.0965
z-value 0.2
P-value 0.8207
Interpretation
Not significant,
accept null hypothesis that
sample proportions are equal
n by pi n * pi >5, test ok

The p-value is given as 0.821 (a value greater than 5% level of significance), we therefore fail to
reject the null hypothesis and conclude that the sample proportions are equal. That is, the
proportion of movies made before 2010 and those made in 2010 - 2019 with a runtime of at least
2 hours are the same.
TASK 3:
In this section, using the chi-square test of independence and a sample of 200 movies released in
2010 - 2019, we sought to test the hypothesis that revenue and budget are related at the 2%
significance level. The revenue data was split into the following three classes; < $50M, $50M to
$100M, and > $100M. The budget was split into the following three classes < $10M, $10M to
$50M, and > $50M.
The hypothesis tested is as follows;
Null hypothesis (H0): There is no significant association between budget and revenue
Alternative hypothesis (HA): There is significant association between budget and revenue.
Results of the test are given below;
Revenue group * Budget group Cross tabulation
Count
Budget group Total
< $10 M >$50 M $10 M to $50 M
Revenue group
< $50 M 37 2 60 99
>$100 M 0 49 20 69
$50 M to $100 M 4 7 21 32
Total 41 58 101 200
Chi-Square Tests