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A hypothesis testing process consists of four consecutive steps that present a logical basis for decision-making concerning the validity of a hypothesis. In particular, the first step is stating the hypotheses, where a null hypothesis implies that there is no relationship between the variables. The alternative hypothesis implies that there is a relationship or dependence in the general population. The second step of hypothesis testing is setting the criteria for the decision. It deals with determining the significance level, which might be either alpha level or critical region. The third step includes the data collection process and sample statistics computing. During the third step, objective data analysis is performed that allows identifying the position of the sample within the set criteria. Finally, the fourth step implies making a decision based on the computed sample statistics results.
Alpha level and critical region are essential in hypothesis testing since the position of the sample in either of these levels predetermines whether the hypothesis is rejected or proven. When making a decision concerning a hypothesis, the researcher should determine how far the sample is from the null hypothesis value to prove the alternative hypothesis. However, if the sample is within the alpha level, it means that a null hypothesis cannot be rejected. On the contrary, if the sample is within a critical region, a null hypothesis is rejected.
If the difference between the sample mean and the original population mean increases, the value of the z-score increases. The increase of the population standard deviation leads to the decrease of the z-score value in hypothesis testing. The z-score value increases with the increase in sample size and the number of scores in the sample.
Null hypothesis: Studying from the screen has no effect on students quiz scores.
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Step 1: Null hypothesis: There is no dependence between screen studying and students quiz scores.
Alternative hypothesis: Students studying from the screen have lower quiz scores. -
Step 2: The null hypothesis might be rejected if the samples final exam score reaches the level of 77, given that the alpha is.05.
Thus, H0: ¼ =77; Ha: ¼ `77. -
Step 3. To calculate the sample statistics, the following z-score formula is used Z = (M-¼)/(Ã/ n). œ stands for the sample mean, ¼ stands for the original population mean, and à stands for standard deviation. Given the values, the calculation of the z-score is as follows: Z= (72.5 77)/(8/4)=-2.25.
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Step 4: Since the alpha level was assumed.05, the identified z-score is placed far from the alpha level, which allows for rejecting the null hypothesis. The testing shows that there is a significant relationship between screen studying and students quiz scores.
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Hypothesis testing: H0: µ = 50; Ha: ¼ ` 50.
To test the hypothesis, the z-score formula should be applied: Z = (M-¼)/(Ã/ n).
Z= (53.8-50)/(15/10) = 2.53.
The evidence is sufficient to make a conclusion that self-esteem scores for these adolescents are significantly different from those of the general population. -
To compute the size of difference using Cohens d, one should divide the mean difference by standard deviation. Thus, 3.8/15=0.25. This value is considered a small effect size.
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The sample provides enough evidence to prove the hypothesis based on the calculated z-score; Cohens d indicates a small size of the difference.
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