Week 7 In-class activity_FA23_Key_v2

Week 7 In-class activity: Hypothesis testing and independent samples t-test 10/5/23 KEY Name: ___________________________ 1. If we fail to reject the null hypothesis, but the null hypothesis is actually false, what type of error are we making? Why might researchers be concerned about making this type of error? We are making a Type II error. In terms of the treatment conclusion, it would mean that we conclude there was not an effect of the treatment, but there really was. The implication of this is that we might be missing out on an effective or new treatment that we could be using to impact a particular outcome variable. 2. If a result is statistically significant, what does this tell us about our treatment in a study? If we know results are statistically significant, why do we need effect size measures? Statistical significance means that our treatment likely had an effect. When we conclude that a result is significant, we are saying that the result (e.g., the mean, mean difference) is very unlikely to have occurred due to sampling error or chance alone. Hypothesis testing and thus statistical significance only tells us if there is an effect or not; effect size measures are important because they tell us the magnitude of our effect (e.g., practical significance). Effect size measures can tell us if our treatment is producing a big or small effect on the outcome of interest. 3. If I report a confidence interval for a sample mean of M = 65 to be 95% CI [62, 68], which of the following best describes the interpretation of the 95% CI? A) 95% of scores in my sample are between 62 and 68. B) I’m 95% sure that the mean for this particular sample is between 62 and 68. C) I’m 95% sure that the true population mean is located between 62 and 68. D) None of the choices are correct. 4. If someone wanted to describe an independent samples t-test, which of the following would be the most accurate description? A) It uses the same group of participants to obtain two sets of scores that can be compared to examine the mean difference. B) It uses two different groups of participants to obtain two sets of scores that can be compared to examine the mean differences. C) It uses one group of participants to evaluate a hypothesis about one population mean. D) None of the choices are correct.

5. A researcher wants to see what kind of candy gives people the most energy. There are 27 people total in the sample. 15 people are given a fun-sized Milky Way bar and 12 different people are given a fun-sized Twix bar. The researcher then counts how many push-ups each participant can do after eating the candy. Milky Way Twix n = 15 n = 12 M = 18 M = 22 SS = 150 SS = 136 Use an independent samples t-test to see whether the number of push-ups differs for people who eat Milky Way versus people who eat Twix. a) Gather the information you need to find the critical value and calculate your test statistic: Mean difference for sample: 18-22 = -4 df total: (15-1) + (12-1) = 14+11 = 25 Pooled variance: s p 2 = SS 1 + SS 2 df 1 + df 2 = 150 + 136 14 + 11 = 11.44 b) What is your critical value for this study? t critical: ± 2.060 c) What is your t-calculated value? s M1 - M2 = √ s p 2 n 1 + s p 2 n 2 = √ 11.44 15 + 11.44 12 = √ 0.76 + 0.95 = 1.31 t = M 1 − M 2 s M 1 − M 2 = ( 18 − 22 ) 1.31 = -3.05 d) Calculate the 95% CI for this study. M 1 − M 2 ± t crit * s M 1 − M 2 95% CI = -4 ± 2.060*1.31 = -4 ± 2.70 = 95% CI [-6.70, -1.30] Note: 2.060*1.31 = 2.70 If you had calculated a mean difference of 4, your 95% CI should be [1.30, 6.70] e) What can we conclude about our results? Make your decision about the null hypothesis and interpret your results in APA style.