Descriptive Statistics and Probability - Basic Statistics

Running head: BASIC STATISTICS
Basic Statistics
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DESCRIPTIVE STATISTICS AND PROBABILITY1
Table of Contents
Solution 1:..................................................................................................................................2
Solution 2:..................................................................................................................................2
Solution 3:..................................................................................................................................3
Solution 4:..................................................................................................................................3
Solution 5:..................................................................................................................................4
Solution 6:..................................................................................................................................5
Solution 7:..................................................................................................................................6
Solution 8:..................................................................................................................................7
Solution 9:..................................................................................................................................7
Solution 10:................................................................................................................................9
Reference..................................................................................................................................10

DESCRIPTIVE STATISTICS AND PROBABILITY2
Solution 1:
Table 1: Summary statistics of pre-treatment scores data
SCORE DATA
Mean 50.07
Median 41
Mode 37
Standard Deviation 22.90
Sample Variance 524.50
Range 79
Minimum 19
Maximum 98
Solution 1.a: The mean for the data is 50.07.
Solution 1.b: The median is 41.
Solution 1.c: The mode is 37.
Solution 1.d: The range is 79.
Solution 1.e: The variance is 524.50.
Solution 1.f: The standard deviation is 22.90.
Solution 2:
Table 2: Chi-square Test
P 0.00
Chi-square 51.4432
Chi-square at 0.05 15.51
Chi-square at 0.01 20.09
Solution 2.a: The Chi-square statistic is 51.4432.
Solution 2.b: At 0.05 level of significance, the null hypothesis is rejected as the critical
value of chi-square at 0.05 is less than the estimated chi-square value.

DESCRIPTIVE STATISTICS AND PROBABILITY3
Solution 2.c: At 0.01 level of significance, the null hypothesis is rejected as the critical value
of chi-square at 0.01 is less than the estimated chi-square value (Pandis, 2016).
Solution 3:
Table 3: Correlation Coefficient
Correlation Coefficients
Pearson 0.83466
Solution 3.a: The Pearson r correlation coefficient for the data is 0.83466.
Solution 3.b: The correlation coefficient says that there is a strong correlation between the
two parameters as the coefficient value is close to 1.
Solution 4:
Solution 4.a:
Table 4: Pearson's coefficient (t test) at .05 significance level
Alpha 0.05
Tails 2
correlation 0.83
standard error 0.13
t 6.43
p-value 0.00
lower 0.56
upper 1.11
The p-value of the t-test is less than 0.05 that indicates that there is enough evidence
to reject the null hypothesis that there is no correlation between the two variables. This means
the alternative hypothesis is accepted that means there exist a positive correlation between the
two variables at 0.05 significance level (Koo & Li, 2016).