# VCU STAT 210 - Test 6 Practice Test #2 (4 pages)

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## Test 6 Practice Test #2

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- Pages:
- 4
- School:
- Virginia Commonwealth University
- Course:
- Stat 210 - Basic Practice of Statistics

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Test 6 Practice Test 2 1 In the current chapter covering statistical inferences on means all of the procedures we have discussed sampling distributions confidence intervals and statistical tests have involved two assumptions What are those two assumptions 2 What is the point estimate of the population mean A Z B X C 0 D s E t F p 3 On November 4 2014 polling locations throughout the United States were open for midterm elections All members of the US House of Representatives were elected as were many US Senators state governors and other local officials Voter turnout for midterm elections is usually smaller than when there is a Presidential election and of interest is the mean amount of time it takes an eligible voter to complete the voting process defined to be the time from entering the voting location to exiting the voting location during a midterm election It is conjectured that the mean amount of time that it takes all eligible voters to complete the voting process during a midterm election is 12 minutes and of interest is to test this conjecture versus the alternative that the mean amount of time that it takes all eligible voters to complete the voting process during a midterm election is different from 12 minutes State the appropriate null and alternative hypotheses that should be tested 4 Consider the information and hypotheses specified in question 3 A simple random sample of 81 eligible voters was selected and the time it took each to complete the voting process was recorded The mean amount of time for this sample of 81 eligible voters to complete the voting process was 10 8 minutes with a standard deviation of 4 1 minutes The distribution of the data was skewed to the right If appropriate use this information to test the hypotheses stated in question 3 at the 10 level of significance 5 In the Commonwealth of Virginia the 7 th congressional district covers much of central Virginia and Dave Brat defeated Jack Trammell to become a new member of the House of Representatives for the 7 th district Of interest is to determine the mean age of all voters who voted in the 7 th congressional district Based on this what is the population of interest 6 Consider the information in question 5 Based on this using both the appropriate symbol and in words what is the parameter of interest 7 Of interest in this problem is to estimate the mean age of all voters who voted in the 7 th congressional district For this problem only assume that the standard deviation of the ages of all such voters is 8 7 years What is the minimum number of voters who voted in the 7th congressional district that would need to be selected for the sample to allow the calculation of a 90 confidence interval with margin of error no larger than 2 6 Please circle your final answer 8 A simple random sample of 41 voters who voted in the 7 th congressional district was selected and the age of each voter was recorded The mean age for this sample of 41 voters was 59 3 years with a standard deviation of 10 4 years and there were a few young people in the sample that skewed the distribution to the left If appropriate use this information to calculate and interpret a 90 confidence interval for the mean age of all voters who voted in the 7th congressional district 9 In question 8 a 90 confidence interval was computed based on a sample of 41 voters If the confidence level were increased to 98 what impact would this have on the margin of error and width of the confidence interval A The margin of error would increase and the width would decrease B The margin of error would decrease and the width would increase C Neither the margin of error nor the width would be affected D Both the margin of error and the width would increase E Both the margin of error and the width would decrease 10 Is the mean age of all voters who voted in the 7 th congressional district in the confidence interval computed in question 8 11 For eligible voters who are unable to vote on election day for example voters who are traveling out of the region or for students away at college the Commonwealth of Virginia allows a person to vote by absentee ballot Suppose it is known that the number of eligible voters per polling location that vote by absentee ballot has a distribution that is heavily skewed to the right with a mean of 29 7 voters and a standard deviation of 7 2 voters If a simple random sample of 64 polling locations in the Commonwealth of Virginia is selected and the number of voters who voted by absentee ballot determined for each describe completely the sampling distribution of the resulting mean number of absentee ballots cast for this sample of 64 polling locations X Test 6 Practice Test 2 Solutions 1 The assumptions are 1 Simple random sample 2 Normal population or large enough sample for the Central Limit Theorem to apply 2 B The sample mean 3 H0 4 1 Hypotheses were stated in question 3 X is the point estimate of the population mean 12 versus Ha 12 10 2 We had a simple random sample and the sample size is large enough for the Central Limit Theorem to apply n 81 15 Therefore the assumptions are satisfied The population standard deviation is unknown the problem gave the value for s so we must use the t distribution X 0 10 8 12 1 2 t s 4 1 0 4556 n 81 2 634 3 p value 2P t80 2 634 2P t80 2 634 2 005 p value 01 01 p value 02 calculator gives 0101 4 Since p value 10 we reject the null hypothesis 5 There is sufficient evidence that the mean amount of time that it takes all eligible voters to complete the voting process during a midterm election is different from 12 minutes 5 The population of interest is all voters who voted in the 7th congressional district 6 The parameter of interest is the mean age of all voters who voted in the 7th congressional district 7 n 8 We have a simple random sample and the sample size is large enough for the Central Limit Theorem to apply n 41 15 so the assumptions are satisfied The population standard deviation is unknown the problem gave the value for s so we must use the t distribution df n 1 41 1 40 90 CI implies t 40 1 684 So Z 2 1 645 8 7 m 2 6 X t 40 2 5 5044 2 30 3 Round up to 31 voters 59 3 1 684 1 6242 59 3 2 74 sn 59 3 1 684 10 4 41 56 56 62 04 Calculator gives 56 565 62 035 We have 90 confidence that the mean age of all voters who voted in the 7 th congressional district is between …

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