Data Analysis: Frequency Table, Histogram, Regression Model and Hypothesis Testing

This article covers data analysis techniques such as frequency table, histogram, regression model and hypothesis testing with examples and interpretations.

Data analysis 1
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Data analysis 2
NO. 1
a. Frequency table
Class Frequency Relative frequency % frequency
123 - 173 9 0.18 18%
174 - 224 15 0.3 30%
225 - 275 11 0.22 22%
276 -326 5 0.1 10%
327 - 377 4 0.08 8%
378 - 428 2 0.04 4%
429 - 479 3 0.06 6%
480 - 530 1 0.02 2%
Table 1
b. Frequency distribution histogram for percentages
123 -
173 174 -
224 225 -
275 276 -
326 327 -
377 378 -
428 429 -
479 480 -
530
0%
5%
10%
15%
20%
25%
30%
35%
% frequency
Class
Frequency
Figure 1
It can be observed that the distribution curve above is not normal. The curve is skewed
to the right. This indicates that the order values are not normally distributed.
c. Since the shape is skewed to the right it means that there are extreme values on
the right. Extreme values always affect the mean hence rendering it unfit for

Data analysis 3
measure. The median is the best measure for this distribution because it is
resistant to outliers.
QUESTION 2
a. The results are F (2, 47) = 74.13, and the p-value tabulated is 0.000. Compared
to alpha value which is 0.05 (greater than p-value), the decision is rejecting the
null hypothesis. It is concluded that demand and price are related.
b. Finding the Coefficient of determination
Coefficient of determination= R egressionS um of S quares
R egressiontotal
= 5048.818
8181.479 =0.617
R-square value of 0.617 means that 61.7% of change in demand is caused by price.
Price is the independent variable while demand is the dependent variable.
The coefficient of correlation
coefficient of correlation= standard error
coefficient of determination
¿ 0.248
0.617 =0.4
QUESTION 3
Hypothesis
H0: The mean of all treatments are equal
Versus
H1: At least one treatment has a different mean
The results are F (2, 23) = 16.43, and the p-value tabulated is 0.000. Compared to
alpha value which is 0.05 (greater than p-value), the decision is rejecting the null
hypothesis. It is concluded that at least one mean is different.

Data analysis 4
QUESTION 4
a. The regression model
y=0.4977 ( X1 ) +0.4733 ( X2 ) + 0.8051
Where y=number of phones sold
X1 =price
X2 =Number of advertising spots
b. Is the model significant
Because F (2,102) = 63.06, p < 0.001. Conclusion: the model is significant at 0.05 level
of significance
c. Test significance of coefficients
Since the p-value 0.001 is less than 0.05, we conclude that 1 and 2 are significantly
different from zero.
d. The slope of number of advertising spots
The slope is 0.4733. It means that one unit change in number of advertising
spots leads to a 0.4733 unit change in phone sales.
e. Number of phones sold
number of phones sold=0.4977 ( 20,000 ) +0.4733 ( 10 ) +0.8051
number of phones sold=9,959.54∨9960