Chapter 7 Ap Statistics Practice Test Answers Joburgore

Chapter 7 Ap Statistics Practice Test Answers Joburgore Chapter 7 AP Statistics Practice Test Answers Joburgore This document provides answers and explanations for a practice test covering Chapter 7 of an AP Statistics textbook focusing on the topic of Inference for Proportions The test is tailored towards students in Johannesburg South Africa denoted by the Joburgore reference The document will be organized as follows 1 Briefly introduce the purpose of the practice test and its relevance to the AP Statistics curriculum Highlight the key concepts covered in Chapter 7 such as confidence intervals hypothesis testing and the Central Limit Theorem for proportions 2 Practice Test Questions and Answers Present each question from the practice test followed by its corresponding answer and a detailed explanation Each answer will be supported with relevant formulas concepts and calculations to demonstrate the reasoning behind the solution 3 Conclusion Summarize the main takeaways from the practice test and emphasize the importance of understanding the concepts related to inference for proportions Encourage further practice and review of the chapter materials to reinforce understanding Practice Test Questions and Answers with explanations Question 1 A researcher wants to estimate the proportion of South African adults who have received at least one dose of a COVID19 vaccine They conduct a random sample of 500 adults and find that 320 have been vaccinated a Calculate a 95 confidence interval for the true proportion of vaccinated adults in South Africa 2 b Interpret the confidence interval in the context of the problem Answer a Step 1 Identify the sample proportion p 320500 064 Step 2 Calculate the standard error SE p1pn 064036500 0024 Step 3 Find the critical value z for a 95 confidence interval Using a ztable the critical value for a 95 confidence level is approximately 196 Step 4 Calculate the margin of error Margin of Error z SE 196 0024 0047 Step 5 Construct the confidence interval Confidence Interval p Margin of Error 064 0047 0593 0687 b We are 95 confident that the true proportion of South African adults who have received at least one dose of a COVID19 vaccine lies between 593 and 687 Question 2 A pharmaceutical company claims that their new flu vaccine is 80 effective A researcher wants to test this claim They randomly sample 200 individuals and find that 145 of them did not contract the flu after receiving the vaccine a State the null and alternative hypotheses for this test b Calculate the test statistic c Determine the pvalue d State your conclusion at a significance level of 005 Answer a Null Hypothesis H0 The vaccine is 80 effective p 08 Alternative Hypothesis H1 The vaccine is not 80 effective p 08 3 b Sample proportion p 145200 0725 Test statistic z z p p p1pn 0725 08 0802200 25 c Pvalue Since the alternative hypothesis is twosided we need to find the probability of getting a test statistic as extreme as 25 or more extreme in either direction Using a ztable the pvalue is approximately 00124 d Conclusion Since the pvalue 00124 is less than the significance level 005 we reject the null hypothesis We have sufficient evidence to conclude that the vaccines effectiveness is different from 80 Question 3 A company conducts a survey of 1000 randomly selected customers to determine the proportion who are satisfied with their recent purchase The survey reveals that 850 customers are satisfied a Calculate the margin of error for a 90 confidence interval for the true proportion of satisfied customers b Explain how the margin of error would change if the sample size were increased to 2000 Answer a Sample proportion p 8501000 085 Standard error SE p1pn 0850151000 0011 Critical value z for a 90 confidence interval z 1645 Margin of error Margin of Error z SE 1645 0011 0018 b Increasing the sample size to 2000 would decrease the margin of error This is because the standard error is inversely proportional to the square root of the sample size A larger sample size leads to a smaller standard error resulting in a narrower confidence interval and a 4 smaller margin of error Question 4 A political pollster wants to estimate the proportion of voters who favor a certain candidate They conduct a poll of 500 randomly selected voters and find that 280 favor the candidate a Construct a 99 confidence interval for the true proportion of voters who favor the candidate b The pollster wants to reduce the margin of error to 2 How many voters should they sample Answer a Sample proportion p 280500 056 Standard error SE p1pn 056044500 0022 Critical value z for a 99 confidence interval z 2576 Margin of error Margin of Error z SE 2576 0022 0057 Confidence Interval Confidence Interval p Margin of Error 056 0057 0503 0617 b Desired margin of error 002 Rearranging the margin of error formula we get n z Margin of Error2 p1p Substituting values n 2576 0022 056044 2401 The pollster should sample approximately 2401 voters to achieve a margin of error of 2 Conclusion This practice test covered several fundamental concepts related to inference for proportions You should be able to calculate confidence intervals for proportions conduct hypothesis tests for proportions and understand the relationship between sample size confidence level and margin of error Remember that inference for proportions is a crucial tool in analyzing data and drawing conclusions about populations Continued practice and review of these concepts will ensure 5 you are wellprepared for the AP Statistics exam and future statistical endeavors