Test 6 Practice Test #21. In the current chapter covering statistical inferences on means, all of the procedures we have discussed (samplingdistributions, confidence intervals and statistical tests) have involved two assumptions. What are those twoassumptions?_____ 2. What is the point estimate of the population mean ?(A) Z (B) ¯X (C) 0 (D) s (E) t (F) ^p3. On November 4, 2014, polling locations throughout the United States were open for “midterm elections”. Allmembers of the US House of Representatives were elected, as were many US Senators, state governors, and otherlocal officials. Voter turnout for midterm elections is usually smaller than when there is a Presidential election, andof interest is the mean amount of time it takes an eligible voter to complete the voting process (defined to be thetime from entering the voting location to exiting the voting location) during a midterm election. It is conjecturedthat the mean amount of time that it takes all eligible voters to complete the voting process during a midtermelection is 12 minutes, and of interest is to test this conjecture versus the alternative that the mean amount of timethat it takes all eligible voters to complete the voting process during a midterm election is different from 12minutes. 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 voterswas selected and the time it took each to complete the voting process was recorded. The mean amount of time forthis sample of 81 eligible voters to complete the voting process was 10.8 minutes, with a standard deviation of 4.1minutes. The distribution of the data was skewed to the right. If appropriate, use this information to test thehypotheses stated in question 3 at the = .10 level of significance.5. In the Commonwealth of Virginia the 7th congressional district covers much of central Virginia, and Dave Bratdefeated Jack Trammell to become a new member of the House of Representatives for the 7th district. Of interest isto determine the mean age of all voters who voted in the 7th congressional district. Based on this, what is thepopulation of interest?6. Consider the information in question 5. Based on this, using both the appropriate symbol and in words, what is theparameter of interest?7. Of interest in this problem is to estimate the mean age of all voters who voted in the 7th congressional district. Forthis problem only, assume that the standard deviation of the ages of all such voters is 8.7 years. What is theminimum number of voters who voted in the 7th congressional district that would need to be selected for thesample to allow the calculation of a 90% confidence interval with margin of error no larger than 2.6? Please circleyour final answer.8. A simple random sample of 41 voters who voted in the 7th congressional district was selected, and the age of eachvoter was recorded. The mean age for this sample of 41 voters was 59.3 years with a standard deviation of 10.4years, and there were a few young people in the sample that skewed the distribution to the left. If appropriate, usethis information to calculate and interpret a 90% confidence interval for the mean age of all voters who voted inthe 7th congressional district._____ 9. In question 8 a 90% confidence interval was computed based on a sample of 41 voters. If the confidencelevel were increased to 98%, what impact would this have on the margin of error and width of theconfidence 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 7th congressional district in the confidence interval computed inquestion 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 adistribution that is heavily skewed to the right with a mean of 29.7 voters and a standard deviation of 7.2 voters. Ifa simple random sample of 64 polling locations in the Commonwealth of Virginia is selected and the number ofvoters who voted by absentee ballot determined for each, describe completely the sampling distribution of ¯X,the resulting mean number of absentee ballots cast for this sample of 64 polling locations.Test 6 Practice Test #2 Solutions1. The assumptions are:1. Simple random sample2. Normal population or large enough sample for the Central Limit Theorem to apply.2. B – The sample mean ´X is the point estimate of the population mean µ.3. H0: μ = 12 versus Ha: μ ≠ 124. (1) Hypotheses were stated in question 3.α = .10(2) We had a simple random sample, and the sample size is large enough for the Central Limit Theorem toapply (n = 81 > 15). Therefore, the assumptions are satisfied. The population standard deviation σ isunknown (the problem gave the value for s), so we must use the t-distribution. t =´X−μ0s√n=10.8−124.1√81=−1.20.4556 = –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 thevoting 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 µ = the mean age of all voters who voted in the 7th congressional district.7. n =(Z¿σm)2=(1.645(8.7)2.6)2 = (5.5044)2 = 30.3; Round up to 31 voters.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 σ is unknown (theproblem gave the value for s), so we must use the t-distribution. df = n – 1 = 41 – 1 = 40; 90% CI implies t40¿ =
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