Hypothesis

Posted: August 26th, 2021

Hypothesis

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Hypothesis

Hypothesis testing relies on the fact that if there is enough of a difference between the experimental sample and the comparison distribution. In this case, the research supports the hypothesis. However, null hypothesis testing is critical in deciding between two interpretations in a statistical relationship for a sample (Gonzalez, 2009). The null hypothesis, denoted by H₀ (H-naught), which implies that there is no relationship within the population and the relationship reflected in the sample, is a sampling error (Gonzalez). The following experiment examines a case where there is a small difference between the experimental sample and the comparison distribution.

Case Experiment

It is estimated that the time boys and girls spent playing sports between the ages of 7 through 11 is the same. An experiment was conducted to confirm the assumption and results presented in the following table;

Table 1: Experiment results

To establish if there is a difference, the analysis is tested at a 5% confidence level.

Results

The study hasan unknown population standard deviation. Let b denote boys and g girls. Then, u_b represents the population mean for boys, while u_g is the population mean for girls. The test is for two independent groups with two population means. The hypothesis is as follows;

H₀: u_b = u_bg-b = 0

Ha: u_b ≠ u_bg-b ≠ 0

Using the student’s –t distribution, the p-value = 0.0054. Hence,

Standard deviation;

Thus, Xb – Xg = 3.1-2 = 1.2, implying that half of the p-value is above 1.2 and a half is below -1.2.

Decision

Given that α> p-value, reject H₀. In this case, reject u_b = u_g implying that there is a difference. The results show that there is a difference, so reject the null hypothesis. However, the difference is minimal at a confidence interval of 5%. Still, it will be possible to reject the null hypothesis even when the p-value = 0.03 or 3% confidence interval.

Reference

Gonzalez, R. (2009). Data analysis for experimental design. New York: Guilford Press.