Statistics Application Problem: Sunspot Analysis 2000/2001

This assignment analyzes sunspot data from the years 2000/2001 to determine if the daily sunspot counts were significantly higher or lower than average. The student first calculated the mean and standard deviation of sunspots from 1700-2014. Then, using the Helioviewer website, the student selected 10 dates during different months in 2000/2001, counted active regions, and recorded the counts. The student then performed a t-test to determine if the average sunspots in 2000/2001 significantly varied from the overall average of 105.95. The t-statistic and p-value were calculated, and the null hypothesis was not rejected. References to relevant research papers are included. The solution demonstrates the application of statistical methods to real-world data analysis, including hypothesis testing and the use of the t-test.

STATISTICS
Application Problem
STUDENT ID:
[Pick the date]

Part C
The requisite hypotheses are indicated as follows.
Null Hypothesis: μ = 105.95 which implies that the average annual sun spots does not vary
from the average of 105.95
Alternative Hypothesis: μ ≠105.95 which implies that the average annual sun spots do vary
from the average of 105.95
Part D
In the given case, it is evident that the population standard deviation is not known which
implies that the suitable test would be a t test. Z test would be used only when the standard
deviation of the population is known which is not the case here as the population standard
deviation has not been presented (Hair et. al., 2015).
Part E
The requisite test statistic has been computed below.
T stat = (119.6 -105.95)/(37.81/280.5) = 1.91
For the above value of t stat and df = 28-1 = 27, the requisite p value for this two tailed test is
0.067.
Considering a significance level of 5%, it is apparent that the p value is greater than the
significance level which indicates that the available evidence would not be sufficient to reject
the null hypothesis and accept the alternative hypothesis (Eriksson and Kovalainen, 2015).
Hence, it may be concluded that the average sun spots in 2000/2001 does not significantly
vary from the average.

References
Eriksson, P. and Kovalainen, A. (2015) Quantitative methods in business research. 3rd ed.
London: Sage Publications.
Hair, J. F., Wolfinbarger, M., Money, A. H., Samouel, P., and Page, M. J. (2015) Essentials
of business research methods. 2nd ed. New York: Routledge.