Your friend brags about his ability to do pull-ups. To demonstrate his skills, h

Step 1
The average pull-ups for men in the United States is 8 reps
Z-test \(\displaystyle\rightarrow\) Z-tests are statistical calculations that can be used to compare population means to a sample's. The z-score tells you how far, in standard deviations, a data point is from the mean or average of a data set. A z-test compares a sample to a defined population and is typically used for dealing with problems relating to large samples \(\displaystyle{\left({n}{>}{30}\right)}\). Z-tests can also be helpful when we want to test a hypothesis. Generally, they are most useful when the standard deviation is known.
t-test \(\displaystyle\rightarrow\) t-tests are calculations used to test a hypothesis, but they are most useful when we need to determine if there is a statistically significant difference between two independent sample groups. In other words, a t-test whether a difference between the means of two groups is unlikely to have occurred because of random chance. Usually, t-tests are most appropriate when dealing with problems with a limited sample size \(\displaystyle{\left({n}{<}{30}\right)}\).
Hypothesis Testing : A statistical hypothesis is an assertion or conjecture concerning one or more populations.
To prove that a hypothesis is true, or false, with absolute certainty, we would need absolute knowledge. That is, we would have to examine the entire population. Instead, hypothesis testing concerns on how to use a random sample to judge if it is evidence that supports or not the hypothesis.
Hypothesis testing is formulated in terms of two hypotheses:
- H0: the null hypothesis;
- H1: the alternate hypothesis
Step 2
z-test because z-test is a statistical test to determine whether two population means are different when the variances are known and the sample size is large. Here, he knows that he can do let suppose 5 number of pull ups and the average of pull ups is 8 per reps, population is large and variance is known thatswhy z-test is used.
b. \(\displaystyle{H}{1}\rightarrow\) The alternative hypothesis, H1 or Ha, is a statistical proposition stating that there is a significant difference between a hypothesized value of a population parameter and its estimated value. The smallest observed significance level for which the null hypothesis would be rejected is referred to as the p-value.
\(\displaystyle{H}{0}\rightarrow\) The null hypothesis (H0) is a statement of “no difference,” “no association,” or “no treatment effect.”
The alternative hypothesis, Ha is a statement of “difference,” “association,” or “treatment effect.” H0 is assumed to be true until proven otherwise. However, Ha is the hypothesis the researcher hopes to bolster.