a) The null hypotheses, mostly denoted by `H_{0}` , is a hypothesis that is to be tested for possible rejection based on the assumption that it is true. Meanwhile, an alternative hypothesis, mostly denoted by the symbols `H_{1}` or `H_{A}` , is one that is accepted when the null hypothesis...

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a) The null hypotheses, mostly denoted by `H_{0}` , is a hypothesis that is to be tested for possible rejection based on the assumption that it is true. Meanwhile, an alternative hypothesis, mostly denoted by the symbols `H_{1}` or `H_{A}` , is one that is accepted when the null hypothesis is rejected; it is the opposite of the null hypothesis. Therefore, the null hypothesis is tested against the alternative hypothesis. For example, if our null hypothesis is `H_{0}` : mean = 75, then the alternative hypothesis can be `H_{1}` : mean > 75 or`H_{1}` : mean < 75 or even `H_{1}` :mean `\ne` 75.

b) A one tailed test is a test in which the entire rejection region is found in only one of the two tails of the sampling distribution of the test statistic, whereas a two tailed test has the rejection region equally divided between the two tails (i.e., it uses both the positive and the negative tails of the distribution). A one tailed test is preferred when you are only interested in an effect in one direction. Meanwhile, a two tailed test is best used when you want to determine any difference between the two groups being compared.

c) Type 1 error occurs when we reject a null hypothesis when it is in fact true, whereas a Type 2 error occurs when we accept a null hypothesis when it is in fact false.

d) A test statistic is a sample statistic that gives the basis for testing a null hypothesis. It is calculated from the sample data and helps us to decide on whether to reject the null hypothesis or not. All the values that a test statistic can take can be divided into two groups: values that are consistent with the null hypothesis and values that are not consistent with the null hypothesis (i.e., they are unlikely to occur should the null hypothesis be true). The former group comprises the acceptance region, and the latter comprises the rejection region or critical region. The critical value, which is based on the level of significance of the test, separates the critical region from the acceptance region. To make conclusions in significance testing, we compare the test statistic with the critical value. If the test statistic is more extreme than the critical value, then the null hypothesis is rejected; otherwise, we fail to reject the null hypothesis.

The p value is the probability of obtaining the observed or even more extreme results when the null hypothesis is true. To make conclusions in significance testing, we compare the p value with the level of significance of the test. If the p value is larger than the significance level, we fail to reject the null hypothesis; however, if the p value is smaller than the significance level, we reject the null hypothesis.

Therefore, the following is a summary of the steps to be followed in hypothesis testing:

- State the problem and specify the null and alternative hypotheses
- Decide on the significance level of the test
- Decide on an appropriate test statistic
- Determine the rejection region
- Calculate the test statistic and p value
- Draw a conclusion.