### Question Description

- Which of the following situations requires independent sample t-tests?
- When comparing an observed mean with a known population mean
- When comparing two sets of observed means obtained from the same group of people
- When comparing two sets of observed means obtained from unrelated groups of people
- When comparing three or more means

- You have a random sample of 35 people who went through a dieting program. You measured their weight before and after they went through the dieting program. You want to know whether the dieting program influenced your weight. What statistical test is the most appropriate test?
- Which of the following is the error term (denominator) used to compute a t-value in a matched pairs sample t-test?
- Standard error of mean computed based on population standard deviation
- Standard error of mean difference computed based on standard deviation of mean difference between the two sets of associated scores
- Standard error of mean computed based on pooled standard deviation of the two samples
- Standard error of mean computed based on sample standard deviation
- Population standard deviation

- In hypothesis testing, alpha represents:
- The risk of Type II error one is willing to take
- The risk of Type I error one is willing to take
- The probability of correctly rejecting null hypothesis
- The probability of correctly accepting null hypothesis

- What is precisely the difference in the situation for independent samples and matched paired samples t-test that lead to different types of computation of t-values.
- Make decisions on whether the following statements are true or false:
- When there are equal number of participants in two conditions, one can always use matched paired sample t-test. True/False
- When there are unequal number of participants in two conditions, one can generally assume that the situation requires independent samples t-tests. True/False
- The difference between whether one can use one sample t-test or other types of t-tests (i.e., independent sample/paired sample) is based on whether one is given a population mean to compare. True/False
- Degrees of Freedom for t-test is always the sample size minus 1 (n-1) irrespective of the type of the t-test. True/False

- Is it okay to use hypothesis testing with t-test when population distribution is not normal. Provide the reason why you think so.
- Explain the difference in error terms used in independent samples and matched paired samples t-tests.
- Which of the two t-tests (independent samples and paired-samples) is more likely to lead to rejection of the Null hypothesis if the data are numerically identical?
- Explain the reason for the answer in 9 above.
- In a study examining whether taking a statistics course influences students reasoning skill, a researcher first gave a reasoning task to 5 students who have never taken a statistics course, and then the students took a brief statistics lecture which lasted 3 hours. After the lecture, the same five students took the reasoning task again. Their performance scores are summarized in the table below.
- In the above (#9), the same 5 students took the test twice, before and after the lecture. Reanalyze the above data as the data obtained from two sets of independent samples. Now please perform an appropriate statistical test to compare the means, pretending that two different (independent) groups of five people took the same test, one before and one after the lecture.

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Student ID |
Performance before the lecture |
Performance after the lecture |

A |
6 |
8 |

B |
7 |
7 |

C |
5 |
7 |

D |
8 |
8 |

E |
7 |
10 |

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Perform an appropriate statistical test and provide your conclusion on whether or not their reasoning performance are different before and after taking the STATS lecture.