Problem set #8 Fall 2023

BIOL 4500 – Introduction to Biological Research Name_________________________ Problem Set # 8 (1) An experiment was conducted to evaluate the effectiveness of a treatment for tapeworm in the stomachs of sheep. A random sample of 60 worm-infected sheep of approximately the same age and health was randomly divided into two groups. Thirty of the sheep were injected with an experimental drug and the remaining 30 were left untreated. After a 6-month period, the sheep were slaughtered and the following worm counts from their small intestines were recorded. Animals infected with a heavy parasite load will often have a lower weight than individuals with a low parasite load or animals free of parasites. Therefore, to further assess the effectiveness of the experimental drug in reducing parasite load, a subset of the sheep given the experimental drug were weighed (in pounds) both before and after the experiment. Analyze the data using the appropriate statistical techniques in SPSS and answer the questions. Drug-treated sheep: 78, 75, 68, 92, 55, 74, 65, 80, 98, 52, 67, 55, 49, 66, 75, 90, 89, 73, 61, 76, 81, 89, 82, 70, 68, 74, 85, 97, 95, 78 Untreated sheep: 71, 70, 66, 85, 60, 72, 57, 75, 92, 56, 63, 52, 48, 67, 70, 88, 80, 65, 60, 74, 76, 78, 78, 62, 73, 73, 75, 88, 94, 75 Initial weight of sheep: 30.20, 40.90, 50.10, 60.30, 70.10, 30.80, 80.10, 70.30, 50.90, 80.90 Final weight of sheep: 30.70, 40.20, 50.40, 50.80, 80.80, 30.40, 40.70, 50.30, 60.80, 70.20 (a) What are the means, standard deviations, standard errors, and variance for the data sets? (2 pts.) Descriptive Statistics N Minimu m Maximu m Mean Std. Deviation Varianc e Statistic Statistic Statistic Statistic Std. Error Statistic Statistic Drugtreated 30 49.00 98.00 75.2333 2.42624 13.28905 176.599 Untreated 30 48.00 94.00 71.4333 2.08590 11.42497 130.530 Valid N (listwise) 30

Descriptive Statistics N Minimu m Maximu m Mean Std. Deviation Varianc e Statistic Statistic Statistic Statistic Std. Error Statistic Statistic Initialweight 10 30.20 80.90 56.4600 5.97216 18.88563 356.667 Finalweight 10 30.40 80.80 50.5300 5.17535 16.36589 267.842 Valid N (listwise) 10 (b) Calculate a 95% Confidence Interval for each mean. (1 pt.) One-Sample Test Test Value = 0 t df Significance Mean Difference 95% Confidence Interva the Difference One-Sided p Two-Sided p Lower Upper Initialweigh t 9.454 9 <.001 <.001 56.46000 42.9500 69.9 Finalweigh t 9.764 9 <.001 <.001 50.53000 38.8225 62.2 Drugtreate d 31.008 29 <.001 <.001 75.23333 70.2711 80.1 Untreated 34.246 29 <.001 <.001 71.43333 67.1672 75.6 (c) State your null (H 0 ) and alternative hypothesis (H a ) for each test you intend to conduct. (2 pts.) Null: There is no difference between the drug treated and the untreated sheep Alternative: There is a greater change between the Drug treated and the untreated sheep (d) Are these tests one-tailed or two-tailed? Why? (2 pts.) One-tailed (e) Are the data normally distributed? What evidence do you have of this? Which test (parametric or non-parametric) is most appropriate in each case? (2 pts.) Tests of Normality Kolmogorov-Smirnov a Shapiro-Wilk Statistic df Sig. Statistic df Sig.

Paired Samples Statistics Mean N Std. Deviation Std. Error Mean Pair 1 Drugtreated 75.2333 30 13.28905 2.42624 Untreated 71.4333 30 11.42497 2.08590 Paired Samples Correlations N Correlation Significance One-Sided p Two-Sided p Pair 1 Drugtreated & Untreated 30 .953 <.001 <.001 Paired Samples Test Paired Differences Mean Std. Deviation Std. Error Mean 95% Confidence Inter the Difference Lower Upp Pair 1 Drugtreated - Untreated 3.80000 4.20509 .76774 2.22979 5 This p value is above .0005 but is still rather low. (h) Determine the power of each test you conducted. Explain what these results mean statistically and biologically. (3 pts.) - The power is above .05 so it is significant to the data. Power Analysis Table Power b Test Assumptions N c Std. Dev. d Effect Size Sig. Test for Mean Difference a .066 30 53.741 .071 .05 a. Two-sided test. b. Based on noncentral t-distribution. c. Number of pairs. d. Standard deviation of the mean difference.