1. (2 marks) Based on the information below, would you reject or accept the null hypothesis? (Assume that the population is normally distributed). Please work through the five steps provided and address the cutoff sample score, Z statistic, and conclusion.

Mean = 5

Standard deviation = 1

Sample score = 7

.05 level of significance one-tailed (directional)

**If you could please walk me through the steps and formulas to do this, please.**

I have the steps, I will include them below but I'm having trouble working through those 5 steps

1. Step one of the hypothesis testing procedures is to find the null hypothesis which is the idea that is being tested based on the data set and is always representative of predicting no relationship between the comparative variables. We then state the alternative or research hypothesis, this hypothesis should include a research prediction with some type of effect or relationship between the two variables that directly contradict the null hypothesis. If the research hypothesis is true, then the other cannot also be true. In hypothesis testing a researcher is not trying to collect data to prove a hypothesis to be true, the researcher is trying to prove one hypothesis must be correct (the research hypothesis) because the alternative has been disprovenby the data of the opposite. (the null hypothesis)
2. The second step is to find the comparison distribution which in hypothesis testing means the data situation if the null hypothesis were proven to be true. This is going to be the data you compare your results to.
3. The third step is to determine the critical value (or cut-off sample score) of the comparison distribution. This is basically asking how careful you want to be with your data, and how tight you want your restriction as for what you will accept as convincing data to reject the null hypothesis.
4. The fourth step is the determine the sample score.

Once the research is concluded and they receive their test results, they convert that data into a z score for the population.

1. The fifth step and final step is to conclude whether the researcher can reject the null hypothesis (Proving the research hypothesis to be correct).

The researcher will now look at the research results in z-score from our previous step and the cut-off z-score comparatively. The researcher may draw distribution and shade the cut-off sample score area before marking the z-score from the collected data. If the Z score falls outside of that area, it is not extreme enough to be significant and the null hypothesis cannot be rejected. However, if the z-score from the collected data is outside of the shaded area, that means the results support the research hypothesis and the null hypothesis has been disproven.