# Psyc 354 homework 6 percentiles and hypothesis testing with z-tests

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**Part I: Concepts**

**Questions 1–4**

**These questions are based on the Nolan and Heinzen reading and end-of-chapter questions.**

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**2) Using the z table in Appendix B, calculate the following percentages for a z score of -0.45**

**2-a)****% above this z score: Answer**

**Work:**

**2-b) % below this z score: Answer**

**Work:**

**2-c) At least as extreme as this z score (on either side):**

**Answer**

**Work:**

**3) Rewrite each of the following percentages as probabilities, or p levels:**

**3-a) 5% = Answer**

**3-b) 95% = Answer**

**3-c) 43% = Answer**

**4) If the critical values, or cutoffs, for a two-tailed z test are -2.05 and +2.05, determine whether you would reject or fail to reject the null hypothesis in each of the following cases: **

**4a) z = 2.23 Answer**

**4b) z = -0.97 Answer**

**5)**

**Imagine a class of twenty-five 12-year-old girls with an average height of 62 inches. We know that the population mean and standard deviation for this age group of girls is m=59 inches, s = 1.5 inches. (Note that this is a z statistic problem.)**

**5a) Calculate the z statistic for this sample (not the z score). Answer**

**5b) How does this sample mean compare to the distribution of sample means? In other words, how does the height of the girls in the sample compare to the height of girls in th general population? Answer**

**6)**

**For the following scenarios, identify whether the researcher has expressed a directional or a nondirectional hypothesis:**

**6a) Social media has changed the levels of closeness in long-distance relationships. **

**Answer**

**6b) A professor wonders whether students who eat a healthy breakfast score better on exams in morning courses than those who do not eat a healthy breakfast. **

**Answer**

**7)**

**For the following scenario, state the null and research hypotheses in both words and symbolic notation. Symbolic notation must include the symbols “****m _{1}” and “**

**m**

_{2}” and a comparison operator (=,**, <, >,**

**,**

**), as described in Nolan and Heinzen (2014). Remember to consider whether the hypothesis is nondirectional or directional.**

**Scenario: A professor wonders whether students who eat a healthy breakfast score better on exams in morning courses than those who do not eat a healthy breakfast.**

Null Hypothesis (H_{0}): Symbolic Notation

**Answer**

Null Hypothesis:

Written Statement

**Answer**

Research Hypothesis (H_{1}): Symbolic Notation

**Answer**

Research Hypothesis:

Written Statement

**Answer**