McClure



219 H Unit 3 Exam – Version AName:______________________________________A recent study finds that out of 433 selected students from the large high school, 121 respond that they enjoy reading for leisure. Which of the following would build a 98% confidence interval to estimate the proportion of students who enjoy reading leisure. 0.28±2.0540.281-0.284330.28±2.3260.281-0.28433z= 0.26-0.280.281-0.28433z= 0.28-0.260.281-0.28433A new hybrid claims to get 40 miles to the gallon (mpg). A random sample of 50 (of these same hybrids) is selected and driven for 90 days. The sample resulted in a mean of 38 miles to the gallon with a standard deviation of 2.4 miles to the gallon. Which type of hypothesis test is appropriate to see if this is evidence that the hybrid car gets less than 40 miles per gallon?1 sample t-test1 proportion z-test1 proportion t-test1 sample z-testA school with a population size of 1,000 students wants to estimate the proportion of students who are interested in joining a club. In a random sample of 20 students, 15 are hoping to join a club. Why is a 1-Proportion Z Interval NOT appropriate for this situation?The population is not 10 times bigger than the sample size (the sample is too big). The sample size is not at least 30 students.The sample mean is not given.The sample does not have at least 10 successes and 10 failures.A headline in October 2016 states “Hillary Clinton expected to win more than 50% of the popular vote.” A pollster conducts a random sample of 50 states and finds 567 of 1052 voter’s plans on voting for Clinton. Which of the following would be the appropriate hypothesis to see if this poll supports the claim that Clinton will win more than 50% of the popular vote?a)H0: p = 0.5H1: p < 0.5b)H0: p = 0.5H1: p ≠ 0.5c)H0: p > 0.5H1: p ≤ 0.5d)H0: p = 0.5H1: p > 0.5A survey of 625 randomly selected students was conducted to determine student opinion about music. The survey reported that 36 percent of the students surveyed preferred country/western music. The survey estimate had a margin of error of 4 percentage points. A margin of error is reported becausea)Students may misunderstand the survey questions.b)Students may intentionally respond incorrectly.c)Sample proportions vary from sample to sample.d)The people doing the survey may have recorded results incorrectly.Write the appropriate formula and any numbers you input into a statistic app or your calculator. A study found that 36 out of 150 randomly selected Nursing students feel burned out. What proportion of the sample feel burned out?What is the margin of error if we are using 90% confidence?Construct a 90% confidence interval for the proportion of nursing students who feel burnt out. Assume all assumptions and conditions are met. Answer with a sentence. Show your work (write formulas, sketch and shade curves, and calculator inputs). Circle your answer. (3pts each)Suppose that a candy company packages a bag of jelly beans whose weight is supposed to be 30 grams, but in fact, the weight varies from bag to bag according to a normal distribution with mean μ = 30 grams and standard deviation σ = 3 gramsWhat is the probability that 8 randomly selected bags of candy have a mean weight of more than 32 grams?What is the probability that 8 randomly selected bags of candy have a mean weight of less than 30.4 grams?There is only a 10% chance the mean weight of the 8 bags is less than what?8)A social scientist is studying the number of text messages sent by students in class. A random sample of students are selected and the number of messages they sent during class times is recorded on their phones. After gathering the results the scientist uses a computer that has statistical apps to obtain the following 1-sample mean t-test summary to test if students send more than 100 text messages a day while in class. Point EstimateStandard errorDFTest StatisticP-value111.35.8585581.92880.0293Write the conclusion using a 0.05 level of significance?9) Pedro saw a headline in a national newspaper: “40% of college students favor taking a week off for Thanksgiving Day.” He wondered if the percentage of students at SAC who favor the extra time added to the semester was more than 40%. To investigate he selected a random sample of 50 students from the 15,000 students at SAC and asked each student if he or she favors a week of vacation for Thanksgiving. 24 of the students in the sample favored adding a week to the semester to accommodate the time off. Because the sample percentage is (24/50)(100) = 48%, Pedro thinks that more than 40% of students at SAC favor taking a week off for Thanksgiving.To see what values of the sample percentage would be expected if the school percentage was 40%, he runs a simulation 100 times and makes the following dotplot:4572001312668.22 .24 .26 .28 .30 .32 .34 .36 .38 .40 .42 .44 .46 .48 .50 .52 .54 .56 Sample Proportion for Null00.22 .24 .26 .28 .30 .32 .34 .36 .38 .40 .42 .44 .46 .48 .50 .52 .54 .56 Sample Proportion for NullIf the percentage were actually 40%, how surprising would it be to see a sample of 48% or more? Justify your answer using the dotplot. Based on his sample data, should Pedro conclude that the percentage of students at SAC who favor taking a week off for Thanksgiving is greater than 40%? Explain why or why not. 10)The USDA will not allow Turkeys to be sold if Arsenic levels in the Turkey’s flesh exceeds 80ppb. A scientist tested 6 turkeys bought at a supermarket and found the following arsenic levels (in ppb):68 75 8193 95 134 Conduct a hypothesis test (significance level of 0.10) to determine if the supermarket should stop selling Turkey’s because of dangerous arsenic levels. 11)Claim:Mean home prices in Arkansas are less than $300,000Name of test: _______________________________________H0:HA:12)Claim: The president’s favorability rating (proportion that approve) is not 38%. Name of test: _______________________________________H0:HA:13) Claim: On average SAC students live less than 15 miles from campus.Name of test: _______________________________________H0:HA:14)Claim: The proportion of Democrats who plan to vote on Election Day is more than 40%.Name of test: _______________________________________H0:HA:BONUS: What sample size should Linh use if she is conducting a survey to if people still watch professional football? She plans on constructing a 90% confidence interval and wants to keep the margin of error below 3.5% (show work on the back and explain). 219 H Unit 3 Exam – Version BName:______________________________________A new hybrid claims to get 40 miles to the gallon (mpg). A random sample of 50 (of these same hybrids) is selected and driven for 90 days. The sample resulted in a mean of 38 miles to the gallon with a standard deviation of 2.4 miles to the gallon. Which type of hypothesis test is appropriate to see if this is evidence that the hybrid car gets less than 40 miles per gallon?1 sample t-test1 proportion z-test1 proportion t-test1 sample z-testA recent study finds that out of 433 selected students from the large high school, 121 respond that they enjoy reading for leisure. Which of the following would build a 98% confidence interval to estimate the proportion of students who enjoy reading leisure. 0.28±2.0540.281-0.284330.28±2.3260.281-0.28433z= 0.26-0.280.281-0.28433z= 0.28-0.260.281-0.28433A school with a population size of 1,000 students wants to estimate the proportion of students who are interested in joining a club. In a random sample of 20 students, 15 are hoping to join a club. Why is a 1-Proportion Z Interval NOT appropriate for this situation?Independence: The population is not 10 times bigger than the sample size (the sample is too big). Normality: The sample size is not at least 30 students.Normality: The sample does not have at least 10 successes and 10 failures.The sample mean is not given.A headline in October 2016 states “Hillary Clinton expected to win more than 50% of the popular vote.” A pollster conducts a random sample of 50 states and finds 567 of 1052 voter’s plans on voting for Clinton. Which of the following would be the appropriate hypothesis to see if this poll supports the claim that Clinton will win more than 50% of the popular vote?a)H0: p = 0.5H1: p > 0.5b)H0: p = 0.5H1: p ≠ 0.5c)H0: p > 0.5H1: p ≤ 0.5d)H0: p = 0.5H1: p < 0.5A survey of 625 randomly selected students was conducted to determine student opinion about music. The survey reported that 36 percent of the students surveyed preferred country/western music. The survey estimate had a margin of error of 4 percentage points. A margin of error is reported becausea)Students may misunderstand the survey questions.b)Students may intentionally respond incorrectly.c)The people doing the survey may have recorded results incorrectly.d)Sample proportions vary from sample to sample.Write the appropriate formula and any numbers you input into a statistic app or your calculator. A study found that 52 out of 150 randomly selected Nursing students feel burned out. What proportion of the sample feel burned out?What is the margin of error if we are using 98% confidence?Construct a 98% confidence interval for the proportion of nursing students who feel burnt out. Assume all assumptions and conditions are met. Answer with a sentence. Show your work (write formulas, sketch and shade curves, and calculator inputs). Circle your answer. (3pts each)Suppose that a candy company packages a bag of jelly beans whose weight is supposed to be 30 grams, but in fact, the weight varies from bag to bag according to a normal distribution with mean μ = 30 grams and standard deviation σ = 3 gramsWhat is the probability that 9 randomly selected bags of candy have a mean weight of more than 31 grams?What is the probability that 9 randomly selected bags of candy have a mean weight of less than 32 grams?There is only a 10% chance the mean weight of the 9 bags is less than what?8)A social scientist is studying the number of text messages sent by students in class. A random sample of students are selected and the number of messages they sent during class times is recorded on their phones. After gathering the results the scientist uses a computer that has statistical apps to obtain the following 1-sample mean t-test summary to test if students send more than 100 text messages a day while in class. Point EstimateStandard errorDFTest StatisticP-value111.35.8585581.92880.0293Write the conclusion using a 0.01 level of significance?9) Pedro saw a headline in a national newspaper: “40% of college students favor taking a week off for Thanksgiving Day.” He wondered if the percentage of students at SAC who favor the extra time added to the semester was more than 40%. To investigate he selected a random sample of 50 students from the 15,000 students at SAC and asked each student if he or she favors a week of vacation for Thanksgiving. 24 of the students in the sample favored adding a week to the semester to accommodate the time off. Because the sample percentage is (24/50)(100) = 48%, Pedro thinks that more than 40% of students at SAC favor taking a week off for Thanksgiving.To see what values of the sample percentage would be expected if the school percentage was 40%, he runs a simulation 100 times and makes the following dotplot:4572001312668.22 .24 .26 .28 .30 .32 .34 .36 .38 .40 .42 .44 .46 .48 .50 .52 .54 .56 Sample Proportion for Null00.22 .24 .26 .28 .30 .32 .34 .36 .38 .40 .42 .44 .46 .48 .50 .52 .54 .56 Sample Proportion for NullIf the percentage were actually 40%, how surprising would it be to see a sample of 48% or more? Justify your answer using the dotplot. Based on his sample data, should Pedro conclude that the percentage of students at SAC who favor taking a week off for Thanksgiving is greater than 40%? Explain why or why not. 10)The USDA will not allow Turkeys to be sold if Arsenic levels in the Turkey’s flesh exceeds 80ppb. A scientist tested 6 turkeys bought at a supermarket and found the following arsenic levels (in ppb):68 75 8498 122 134 Conduct a hypothesis test (significance level of 0.10) to determine if the supermarket should stop selling Turkey’s because of dangerous arsenic levels. 11)Claim:Home prices in Arkansas are more than $400,000Name of test: _______________________________________H0:HA:12)Claim: The president has increased her favorability rating (proportion who approve) to above 36%. Name of test: _______________________________________H0:HA:13) Claim: On average students live more than 5 miles from SAC. Name of test: _______________________________________H0:HA:14)Claim: The proportion of Democrats who plan to vote on Election Day is not 40%.Name of test: _______________________________________H0:HA:BONUS: What sample size should Linh use if she is conducting a survey to if people still watch professional football? She plans on constructing a 90% confidence interval and wants to keep the margin of error below 3.5% (show work on the back and explain). ................
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