# Statistical Hypothesis Test

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Question 1 A t- test is a statistical hypothesis test in which the test statistic follows a t-distribution if the null hypothesis is acknowledged. Besides, it is widely used in situations whereby the test statistic follow a normal distribution and the value of a scaling term in the test statistic are known. Null hypothesis Î¼ = 39 Alternative hypothesis Î¼ 39 From this analytic calculation it is clear that both the null and alternative hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small. For this analysis, the significance level is 0.01. The test method is a one sample t-test. t- Test = difference between the means Variance Sample size = 13.41-12.38 3.38 40 = 1.03 3.38 40 = 0.007618 Since we have a one tailed test, the t-value is the probability that the t-score having 39 degrees of freedom is greater than -0.894 so there is no need to use the t-distribution calculator to find the value of t. The degree of freedom (DF) is equal to the sample size (n) minus one. Thus, DF = n - 1.Since the t-value (0.007) is lower than the significance level (0.01), we therefore reject the null hypothesis and pick the alternative hypothesis. Besides, this approach is appropriate because the sampling method is a simple random sampling, and the population is normally distributed. Question 2 Dependent samples also known as paired t-tests consist of a group of units that has been tested twice. Dependent t-tests