Berry Makaela HW 7

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Apr 3, 2024

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HOME WORK #7 • Read Chapter 6 from your text and the power-point to answer the following questions. • When doing the HW, please keep the numbering and the questions as it appear on the original HW. You can include your answer next to each question. Most of you followed this, but this is for the few who did not. • Upload the completed HW assignment as a word file or a pdf in the appropriate place in Brightspace. Please DO NOT email me your HW. • Remember to name your file with your first name-Last name and the HW#. Just a note Chapter 4- One sample z-test and one sample z-interval Chapter 5-Two sample t-test and two sample t-interval (independent samples) Chapter 6-Matched paired t-test (dependent samples) 1. As mentioned in the text (page 128), what are the two statistical tests we can use to compare matched-paired data (dependent groups). (a) paired t test (b) Wilcoxon matched-pairs test 2. Fill in the blanks using “parametric test” or “non-parametric test”. Paired t-test is a parametric test and the Wilcoxon matched-Paired Signed Rank test is a non- parametric test . 3. When considering paired t-test and the Wilcoxon matched-Paired Signed Rank test, which has fewer assumptions? Wilcoxon 4. Read the section, “Does breast feeding affect bone density?” in page 129. (a) What are the two related groups in the study? Bone density and bone density (b) What is the grouping variable (intervention)? Twin database (c) In the study what is the researchers’ main question of interest? Does breast-feeding affect bone growth? 5. Read the section, “Does a depression education program change the knowledge base of residents in obstetrics and gynecology?” in page 129. (a) What are the two related groups in the study? Depression education and knowledge base

(b) What is the grouping variable (intervention)? Residents in obstetrics and gynecology (c) In the study what is the researchers’ main question of interest? Does a depression education program change the knowledge base of residents in obstetrics and gynecology? 6. Read the section, “Does a minimal-contact intervention promote walking among sedentary women?” in page 129. (a) What are the two related groups in the study? Minimal contact intervention and walking (b) What is the grouping variable (intervention)? Sedentary women (c) In the study what is the researchers’ main question of interest? Does a minimal-contact intervention promote walking among sedentary women? 7. As in BOX 6-1 page 130, list the conditions that need to be satisfied to perform paired t-test or the Wilcoxon matched-Paired Signed Rank test. The paired t test can be used when There are two paired measurements of the characteristic of interest (i.e., either one pretest and one posttest measurement on the same person or one measurement on a participant and one measurement on a matched control). The two measures that are compared are normally distributed, or there are at least 30 pairs and a distribution that is not too badly skewed. The measurement scale is either interval or ratio (sometimes ordinal is alright as well). The Wilcoxon matched-pairs test can be used when There are two paired measurements of the characteristic of interest (i.e., either one pretest and one posttest measurement on the same person or one measurement on a participant and one measurement on a matched control). The measurement scale of the characteristic is ordinal, interval, or ratio. The total sample size contains at least five pairs of measurements. 8. Consider the example in pages 131-136 and the power-point slides and complete the following steps (highlighted in yellow). Let µ 1 − µ 2 = µ d STEP 1: State the hypothesis H 0 : µ d = 0 vs. H a : µ d ≠ 0 STEP 2 : State the level of significance α - level = 0.05 STEP 3 : Check whether assumptions are met to do a paired t-test. • There are two paired measures of the dependent variable. • Data are approximately normally distributed.

STEP 4 : Compute (or list if they are given to you) Number of pairs n = 31 Group 1 - Pretest Sample mean x 1 = 69.26 Sample standard deviation S 1 = 8.61 Group 2 - Posttest Sample mean x 2 = 78.29 Sample standard deviation S 2 = 6.21 STEP 5 : Calculate the paired test statistic t= -6.935 STEP 6: make a conclusion α -level = 0.05 p-value = 0.000 or p<0.001 Make a conclusion based on your p-value and α -level: Reject null hypothesis 9. Do “Computational Problems” question #1 (only the two paired t-test) in your text (page 148). Complete the following steps (highlighted in yellow). STEP 1: State the hypothesis H 0 vs. H a H0- Fun is not determined by hair color HA-Fun is determined by hair color STEP 2 : State the level of significance α -level = 0.05 STEP 3 : Check whether assumptions are met to do a paired t-test. • There are two paired measures of the dependent variable. • Data are approximately normally distributed. STEP 4 : Compute (or list if they are given to you)

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Number of pairs n = 10 Group 1 – Brown hair Sample mean x 1 = 2.9 Sample standard deviation S 1 = 1.9 Group 2 – Blond Hair Sample mean x 2 = 4.9 Sample standard deviation S 2 = 0.88 STEP 5 : Calculate the paired test statistic t= 3.87 STEP 6: make a conclusion α -level = 0.05 p-value = 0.004 Make a conclusion based on your p-value and α -level: Reject null hypothesis 10. Do “Computational Problems” question #2 (only the paired t-test) in your text (page 148). Complete the following steps (highlighted in yellow). STEP 1: State the hypothesis H 0 vs. H a H0-There is no relationship between which salad is preferred. HA- There is a relationship between which salad is preferred. STEP 2 : State the level of significance α -level = 0.05 STEP 3 : Check whether assumptions are met to do a paired t-test. • There are two paired measures of the dependent variable. • Data are approximately normally distributed. STEP 4 : Compute (or list if they are given to you)

Number of pairs n = 10 Group 1 – Salad A Sample mean x 1 = 8.4 Sample standard deviation S 1 = 4.70 Group 2 – Salad B Sample mean x 2 = 11.3 Sample standard deviation S 2 = 3.30 STEP 5 : Calculate the paired test statistic t= 2.24 STEP 6: make a conclusion α -level = 0.05 p-value = 0.052 Make a conclusion based on your p-value and α -level: Accept null hypothesis 11. Do “Choosing the best statistical test” questions 1-10 in your text (pages 146-147). 1. c 2.d 3.b 4.a 5.b 6.c 7.a 8.a 9.d 10.c

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