Frequency Distribution, Hypothesis Testing, Regression Analysis

This article covers solved examples on frequency distribution, hypothesis testing, and regression analysis. It includes formulas, test statistics, P-values, and interpretations. The subject is not mentioned. The course code, course name, and college/university are not mentioned.

Answer 1
(a) The frequency distribution, relative frequency distribution, and percent frequency
distribution is given below:
Bin Frequency
distribution
Relative frequency
distribution
Percent frequency
distribution
120 0 0 0.00%
170 8 0.16 16.00%
220 15 0.3 30.00%
270 12 0.24 24.00%
320 4 0.08 8.00%
370 5 0.1 10.00%
420 2 0.04 4.00%
470 2 0.04 4.00%
520 2 0.04 4.00%
Total 50 1 100.00%
(b) The histogram of percent frequency distribution is given below:
120 170 220 270 320 370 420 470 520
0.00%
5.00%
10.00%
15.00%
20.00%
25.00%
30.00%
35.00%
0.00%
16.00%
30.00%
24.00%
8.00%
10.00%
4.00% 4.00% 4.00%
Class
Frequency
The maximum of the furniture values belongs to the left side and tail at the right side, so
data is positively skewed.
(c) The median would be best measure for skewed data because it does affected by
outliers.
Answer 2
(a) The null hypothesis is, and the alternate hypothesis is .
The t- test will be used to test the hypothesis. The test statistic value is calculated below:
The, P-Value is calculated in Excel which is (0.000) is less than the 5% level of
significance, so the null hypothesis of the test gets rejected.
Hence, demand and unit price are related.
(b) The value of is . The value of R-Square indicates
that 61.7% of the variation in demand can be explained by the unit price in the model and
rest of the variation remains unexplained.
(c) The coefficient of correlation is . So, the value of the
correlation coefficient is 0.7855, which indicates a strong positive relationship between
demand and the unit price. As, the unit price increases demand also increases.
Answer 3
The formulas of the completely randomized design is given below:
Source of variation Sum of
squares
Degrees of
freedom
Mean square F-
Statistic
Between
Treatments
SSTR
Within Treatments SSE
Total SST
The required values are calculated below:
Source of
variation
Sum of
squares
Degrees of
freedom
Mean square F-Statistic
Between
Treatments
390.58
Within
Treatments
158.40
Total 548.98 23
The P-value is calculated in Excel, the P-Value (0.000) is less than the 5% level of
significance, so the null hypothesis of the test gets rejected. Hence, there is statistically
significance difference among the means of the three populations.

Answer 4
(a) The estimated regression equation relating Y to and is given below:
(b) The null hypothesis for the test is . And, the alternative hypothesis is
. The value of F-test statistic is,
The, P-Value calculated in excel, the P-Value is (0.000) is less than the 5% level of
significance, so the null hypothesis of the test gets rejected. Hence, there is a significant
relationship between all independent variables and dependent variables.
(c). The null hypothesis is, and the alternate hypothesis is .
The t- test will be used to test the hypothesis. The test statistic value is calculated below:
The, P-Value calculated in Excel which is (0.000). The P-value is greater than the 5%
level of significance, so the null hypothesis of the test does not get rejected. Hence, is
not different from 0.
The null hypothesis is, and the alternate hypothesis is .
The t- test will be used to test the hypothesis. The test statistic value is calculated below:
The, P-Value calculated in excel which is (0.000). The P-value is is greater than the 5%
level of significance, so the null hypothesis of the test does not get rejected. Hence, is
different from 0.
(d) The estimated slope for advertising sports is 0.4733, the slope indicates that as
the advertising sports increases by 1 the mobile phone sold per day will increases by
0.4733 percentages.
(e) The predicted value of mobile phones that will be sell is,
Hence, about 15 mobile phones that would be sell if company charges $20000 using 10
advertising sports.