Section 9 Lab Part 1 Intro and Proportions Key

STAT 3090 S ECTION 9 L AB P ART 1 F ALL 2023 H YPOTHESIS T EST (I NTRODUCTION AND P ROPORTIONS ) You are asked to perform a hypothesis test at the 1% significance level to determine if the percentage of employees wearing contact lenses is more than 11%. You take a random sample of 75 employees. The following are the results Frequency Relative Frequency Wear Contacts 15 0.20 Do Not Wear Contacts 60 0.80 Total 75 1.00 Use the following steps to perform this hypothesis test using the Rejection Region approach. (a) Define p in the context of the problem and state the appropriate hypotheses. (5 pts) Let p = the true proportion of Delectable Delight employees who wear contact lenses. H 0 : p = 0.11 H a : p > 0.11 1 pt for defining p in context 1 pt for using p in the hypothesis statements 1 pt for correct value of p 0 1 pt for equal sign in null hypothesis 1 pt for less than sign in alternative hypothesis (b) State and check the conditions for a hypothesis test of a proportion. (4 pts) a) The sample was randomly selected b) The sampling distribution of ^ p is approximately normally distributed since n p 0 = 75 ( 0.11 )= 8.25 ≥ 5 and n ( 1 − p 0 )= 75 ( 0.89 )= 66.75 ≥ 5 2 points for checking a random sample was used 2 points for determining that the sampling distribution of ^ p is approximately normal using the correct reasoning. (c) Calculate the appropriate test statistic. Show how to correctly fill in the formula, then use your calculator do find the test statistic. (5 pts) z 0 = ^ p − p 0 √ p 0 ( 1 − p 0 ) n = 0.2 − 0.11 √ 0.11 ∗( 1 − 0.11 ) 75 = 2.49 3 points for correctly filling in formula – deduct 1 point per mistake 2 pts for correct answer Deduct 1 point for minor arithmetic error 3