Hypothesis Testing Using t-Distribution: Iguana Data Analysis

Meenatchi Ganeshkumar BIOL 528 March 1, 2024 Assignment 4 Submit via Canvas by Sunday 11:30pm Late assignments NOT ACCEPTED This homework assignment will focus on using the t-distribution in hypothesis testing. You will be asked to conduct a series of hypothesis tests using a dataset provided. The dataset you will use is a sampling of the Little Cayman Rock iguana ( Cyclura nubila caymanensis ) that nests in the Cayman Islands (data from T.Miller). For more information on this species visit the National Trust for Cayman Islands website . A sampling of 11 iguana nests found varying number of eggs. The data is provided in an excel sheet. The formulas you will use in this Homework are: (Refer to the key Terms Chapter 9 document on BB) t-statistic formula: t s = x − μ 0 s √ n Confidence interval using t-distribution CI = x± ( t ( α , n − 1 ) ) ∗ s x 1. Researchers hypothesize that if female iguanas were to lay an average of 51 eggs in a brood this would be enough to sustain the population. Using the t-distribution (assumptions of the test are met – see Hampton p. 77) conduct the following hypothesis test given the information provided below. H 0 : μ = 51 Use a two-tailed t-test, alpha=0.10 H a : μ≠ 51 Alpha: 0.10 Choose the test: two – tailed t test Find the t-crit (Table A.2): +/- 1.812 Compute the test Statistic: SE: 3.0005 T-calc: -1.94 Compare your t-calc with your t-crit: (use the t-distribution chart located on excel sheet: copy and past

Meenatchi Ganeshkumar BIOL 528 March 1, 2024 Decision: The null hypothesis is rejected Interpretation: At the alpha of 0.10 the t calc was in the rejection zone , it has been proven from the decision that was concluded from the two tailed t-test the iguanas need to produce more that 51 eggs to stable the population. 1b) Using the sample mean and the t-distribution construct a 90% confidence interval using the data provided above. Reminder: CI = x± ( t ( 0.10 , n − 1 ) ) ∗ s x Upper Limit: 50.62 Lower Limit: 39. 73 1c) Does your 90% CI include 51 eggs? Does your CI support the findings you have from your hypothesis test? No, the 51 eggs do not count towards the 90% confidence interval. It does confirm our findings, because the top limit is just below 51 eggs, indicating that 51 eggs are required for sustainability, hence the brood produced 2. Re-examine the Iguana data and the null hypothesis stated in question #1; however, this time use an alpha level of 0.05. H 0 : μ = 51 Ha: μ≠ 51 Alpha: 0.05 Choose the test: 2 tailed t-test

Meenatchi Ganeshkumar BIOL 528 March 1, 2024 Find the t-crit (Table A.2): +/- 2.228 Compute the test Statistic: SE: 3.0005 T-calc: -1.935 Compare your t-calc with your t-crit: (use the t-distribution chart located on excel sheet: copy and paste) Decision: It failed to reject the null hypothesis Interpretation: 51 eggs can be produced in a sustainable population of iguanas. 2b) Using the sample mean and the t-distribution construct a 95% confidence interval using the data provided above. Reminder: CI = x± ( t ( 0.05 , n − 1 ) ) ∗ s x Upper Limit: 51.88 Lower Limit: 38.49 2c) Does your 95% CI include 51 eggs? Does your CI support the findings you have from your hypothesis test?

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Meenatchi Ganeshkumar BIOL 528 March 1, 2024 This confidence interval does include 51 eggs, so it supports our null hypothesis that 51 eggs can sustain the iguana’s population 3. Over an 8 year period, a large farm just under 6 miles north of Clear Lake, Iowa obtained a yield of 206.66 bushels of corn per acre using a certain variety of seed. Last year a genetically modified variety, costing slightly more, was planted in 10 one-acre test plots with similar growing conditions in a nearby farm. The farm yields are shown on your excel sheet under worksheet “farm yields” If you want to be 95% sure that the new seed is BETTER before you take the added expense, will you switch or not? Use the Hypothesis testing steps. You must decide if this will be a 1 tailed t-test or a 2 tailed t-test. H 0 : μ o ≤ 206.66 Ha: μ a > 206.66 Alpha: 0.1 Choose the test: One tailed t-test Find the t-crit (Table A.2): 1.833 Compute the test Statistic: SE: 7.907 T-calc: 3.204 Compare your t-calc with your t-crit: (use the t-distribution chart located on excel sheet: copy and paste)

Meenatchi Ganeshkumar BIOL 528 March 1, 2024 Decision: Rejecting the null hypothesis Interpretation: At the alpha of 0.05 , the average yield of the GMO corn is greater than 206.66 bushels. It would be recommended that to use GMO should be used only with higher yield.

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