# Sampling, Variables, Hypotheses, Errors, Significance

### Assessment Instructions

Answer the questions below, following the Submission Requirements as specified at the end of the assessment. To calculate t when needed, refer to the T-Table for Assessment 3 document linked in the Resources under the Required Resources heading.

Question | Topic |
---|---|

Question 1 | Independent Variables (IVs) and Dependent Variables (DVs) |

Question 2 | Hypotheses |

Question 3 | Errors and Significance: Type 1 and Type 2 Error |

Question 4 | Errors and Significance: Type 1 and Type 2 Error |

Question 5 | Hypothesis Testing and the z Score |

Question 6 | Standard Error of the Mean |

Question 7 | Central Limit Theorem |

Question 8 | Normal Deviate Z Test |

Question 9 | One Sample t Test |

Question 10 | SPSS: One Sample t Test |

Question 11 | Confidence Intervals |

#### Question 1

A researcher randomly assigns a group of adults to one of two diet plans (Diet Plan A or Diet Plan B). The researcher then measures the amount of weight loss each participant experiences in a two-week period. What are the IV and the DV in this study?

#### Question 2

A researcher is studying whether the amount of weight loss differs in participants who follow Diet Plan A versus those who follow Diet Plan B. Write the following:

- A directional research hypothesis.
- A nondirectional research hypothesis.
- The null hypothesis.

#### Question 3

In the general population, it is an established fact that men weigh, on average, more than women. For your study, you randomly sample 100 men and 100 women, recording each participant’s weight, and you find no significant difference in weight based on gender. What type of error is this (Type 1 or Type 2), given that a difference really does exist in the population? Explain your answer.

#### Question 4

In general, men and women do not differ on IQ. However, as part of your study, you found that women scored significantly higher than men on IQ. Given that you found a difference in your study where none exists in the general population, identify the error (Type 1 or Type 2) and explain your answer.

#### Question 5

Joan is 72 inches tall. The average (mean) height for adult women is 65 inches, and the standard deviation is 3.5 inches. Complete the following:

- State the null hypothesis.
- State the alternative hypothesis.
- State the percentage of women of which Joan is taller, compared to the population (Hint: think z score and area under the normal curve).
- State whether or not you expect to reject the null hypothesis, given Joan’s height as compared to the population mean. Explain your answer.

#### Question 6

College students in a large psychology class take a final exam. The mean exam score is 85, and the standard deviation is 5. Using the formula for σ_{M} , identify the standard error of the mean (σ_{M}) under the following conditions:

- The sample size is 25.
- The sample size is 16.
- The sample size is 20.

#### Question 7

As part of a large research study, you administer a new test to 20,000 adults. Before you record or analyze the data, can you assume that the sampling distribution of the mean for this test will be normally distributed? Why or why not?

#### Question 8

The average (mean) height for adult women is 65 inches, and the standard deviation is 3.5 inches. Given the women you know, you think this number is low, so you record the heights of 25 of your female friends. The average height of your 25 friends is 66.84 inches. If your friends are just a representative sample of adult females, what is the probability that your friends are so tall?

z | Area | z | Area | z | Area | z | Area |
---|---|---|---|---|---|---|---|

1.92 | .9726 | 2.27 | .9884 | 2.62 | .9956 | 2.97 | .9985 |

1.93 | .9732 | 2.28 | .9887 | 2.63 | .9957 | 2.98 | .9986 |

1.94 | .9738 | 2.29 | .9890 | 2.64 | .9959 | 2.99 | .9986 |

#### Question 9

The average (mean) height for adult women is 65 inches, and the standard deviation is 3.5 inches. Given the women you know, you think this number is low, so you record the heights of 9 of your female friends. Below are their heights in inches:

65, 67, 62, 67, 59, 68, 69, 70, 67.

Complete the following:

- State the nondirectional hypothesis.
- State the critical t for α = .05 (two tails).
- Calculate t. Show your work.
- Answer if the height of your nine friends is significantly different than the population mean. Explain.

Remember, you must show all your work to receive credit.

#### Question 10

Complete the following steps:

- Open the SPSS file assessment3a.sav linked in the Resources under the Required Resources heading.
- At the top of the screen, click on Analyze, select Compare Means, then select One-Sample t Test.
- Click on Height, then click on the arrow to send it over to the right side of the table. In the small box labeled Test Value, enter 65.
- Click OK, and copy and paste the output to your Word document.
- Compare your SPSS output to your hand calculations from question 9. Are they the same?

#### Question 11

Based on the SPSS output from Question 10 above, and the test value (population mean) of 65, calculate the 95 percent confidence interval.

#### Submission Requirements

- Submit all answers in one Word document (do not submit multiple files).
- Show your work for questions that require calculations.
- Ensure your answer to each problem is clearly visible (you may want to highlight your answer or use a different font color to set it apart).