Null hypothesis (HO) - Average temperature six months after the birth month is inversely proportional to average age starting to crawl.
Alternative hypothesis (HA) - Average temperature six months after the birth month is not inversely proportional to average age starting to crawl.
The Meaning of the Hypothesis
Hypothesis testing in statistics proves to be a crucial tool for any researcher. It aims at stating that a given population parameter has an equivalent value as reported by the researcher. There are two different types of hypothesis; the null and alternate hypotheses (Goos & Meintrup, 2016). The null hypothesis is one in which the researcher or scholar aims at disproving or nullifying through statistic methods. It thus portrays the general or overview of the subject and the researcher must try to reject it in his or her study. Unlike the null hypothesis, in the alternate hypothesis, the researcher makes a claim in which he tries to support as the cause of the subject under study (Walker & Almond, 2010). In the case of the study, the hypothesis statement implies that under the null hypothesis, the researcher believes that there is an indirect relationship between the changes in temperature immediately after six months from the month of birth. However, the alternative hypothesis rejects this assertion by positing that there exists no indirect relationship between temperature and age parameters of the population. It is the aim of this paper to prove the assertion.
Based on the above assertions, it is necessary to test the hypothesis using the data in the table below;
Table 1: Average Age and Temperature Data
Month Average Age Starting to Crawl (weeks) Average Temperature 6 Months After Birth Month (in units Fahrenheit)
January 29.84 66
February 30.52 73
March 29.7 72
April 31.84 63
May 28.58 52
June 31.44 39
July 33.64 33
August 32.82 30
September 33.83 33
October 33.35 37
November 33.38 48
December 32.32 57
Using the hypothesis test for the population mean, the following output reveals the results of the analysis;
Table 2: t Test: Paired Two Sample for Means
Average Age Starting to Crawl (weeks) Average Temperature 6 Months After Birth Month (in units Fahrenheit)
Mean 31.77 50.25
Variance 3.099 251.11
Observations 12 12
Pearson Correlation -0.699
Hypothesized Mean Difference 0
t Stat -3.737
P(T<=t) one-tail 0.00164
t Critical one-tail 1.795
P(T<=t) two-tail 0.00327
t Critical two-tail 2.2009
Table 2 is a summary statistics showing results of hypothesis test. The mean value is 31.77 and a variance of 3.099 for the average age starting to crawl while the mean is 50.25 and a variance of 251.11 for the average temperature six months after birth month. Using a two tail t-Test, the results shows that calculated t is 0.00327 or p value = 0.00327 while t Critical is 2.2009. Since the pvalue < 0.05 or tcalculated is less than t Critical, we fail to reject the null hypothesis. This confirms that there is an indirect relationship between average age starting to crawl and average temperature after birth month (Goos & Meintrup, 2016). Hence, through hypothesis test, it is possible to ascertain the true statement as asserted by both the null and the alternative hypothesis. However, this can only be achieved when there is proper interpretation and use of appropriate analytical tools.
Goos, P. & Meintrup, D. (2016). Statistics with JMP: hypothesis tests, ANOVA, and regression. Chichester, West Sussex: Wiley.
Walker, J. & Almond, P. (2010). Interpreting statistical findings: a guide for health professionals and students. Maidenhead New York: Open University Press McGraw Hill.
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