Group Assignment 3 - CI for p & Chi-square Test

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Northern Kentucky University *

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205

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Statistics

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Apr 3, 2024

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1 STA 205 Group Assignment 3 - Confidence Interval for the Proportion & Chi-Square Hypothesis Tests Directions: Handwrite your answers and all supporting work on a separate piece of paper. Be sure your work is clearly written and organized, labeling each question number and part. Take photos or scan your work and save as a single PDF file for submission. 1. Medical researchers seek to estimate the percentage of people with ADHD. In a random sample of 1,562 people, 55 have ADHD as defined by the researchers. a. What variable is recorded for each individual sampled? Classify the variable as categorical or quantitative. b. Estimate the proportion of with ADHD using 95% confidence. (Round decimal calculations to four decimal places.) c. If the previous estimate is used and the confidence level remained the same, what size sample should be used to have margin of error within ± 3%? d. Does the interval calculated in part b support that claim the percentage of people that have ADHD is different than 4%? Explain. e. Suppose the following hypotheses had been tested: H 0 : p = 0.04 H a : p ≠ 0.04 Based on your answer to part d , would the probability associated with this test be above or below 0.05? Explain your answer without calculating the actual probability. 2. For each statement below, determine whether it is true or false. a. For a 99% confidence interval, the larger the sample size the larger the margin of error. b. In general, a confidence interval is calculated using the following: point estimate ± margin of error. c. A 95% confidence interval is wider than a 90% confidence interval.

2 3. A new study sought to examine the relationship between eating dairy and having eczema. A sample of 455 US adults were selected to participate in the study. Participants were randomly assigned to one of two groups. One group ate dairy every day and the other group ate no dairy. After one month, it was recorded if the individual had eczema on their body. The results are summarized in the StatCrunch output below. a. Compute the number of individuals in the dairy group one would expect to have eczema if there is no relationship between eating dairy and having eczema. b. Within each group, find the percentage of people with eczema. i. The percentage of those in the dairy group that had eczema is ____________%. ii. The percentage of those in the no dairy group that had eczema is ____________%. c. Use the StatCrunch output to conduct the appropriate hypothesis test to determine if there is a relationship eating dairy and having eczema at the 0.1 significance level. Contingency table results: Rows: Group Columns: None Cell format Count (Expected count) (Contributions to Chi-Square) Eczema No Eczema Total Dairy 20 (0.13) 199 (0.01) 219 No Dairy 25 (0.12) 211 (212.66) (0.01) 236 Total 45 410 455 Chi-Square test: Statistic DF Value P-value Chi-square 1 0.602

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Group Assignment 3 - CI for p & Chi-square Test

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