1.To combat red-light-running crashes, many states are installing red light cameras at dangerous intersections. These cameras photograph the license plates of vehicles that run red lights and automatically issue tickets. How effective are these photo enforcement programs? The Virginia Department of Transportation (VDOT) conducted a comprehensive study of its newly adopted program and published the results in a 2012 study. In one portion of the study, VDOT provided crash data both before and after installation of the cameras at several intersections. The data, measured as the number of crashes caused by red light running per intersection per year, for 13 intersections in Fairfax County are given in the first columns in the Minitab file.
What is (are) the parameter(s) we are conducting inference on? Choose one of the following symbols (m; mD(the mean difference from a matched pairs design);m1 - m2 (the mean difference from independent samples); p, or p1 - p2) and describe it in words.
Depending on your answer to part (a), construct one or two probability plots and one or two boxplots to visualize the distribution(s) of your sample data. If you construct two probability plots and two boxplots, please construct two separate Minitab probability plots and one Minitab boxplot displaying both boxes on the same graph. Also, properly title and label your graphs. Copy and paste these graphs into your assignment. Below the graphs, answer the following questions.
- Are there any major deviations from normality?
- Are there any outliers present?
- Is it appropriate to conduct statistical inference procedures, why or why not?
- If the answer to part iii is no, do not complete the rest of #1.
- At the 0.01 significance level, test the claim that the installation of the cameras decreased the mean number of crashes at these particular intersections.
- State the null and alternative hypotheses.
- State the significance level for this problem.
- Calculate the test statistic (subtract after - before)
- Calculate the P-value and include the probability notation statement.
- State whether you reject or do not reject the null hypothesis.
State your conclusion in context of the problem (i.e. interpret your results).
For the above situation, construct a 96.2% confidence interval for the above data. Interpret the confidence interval as we learned in class.Scientists can use high-performance liquid chromatography to determine the amount of drug in a tablet. Twenty-five tablets were produced at each of two different sites. Drug concentrations, measured as a percentage, for the tablets produced at the two different sites are found in column C6 and C7 in the Minitab data file. At the 0.05 significance level, can a researcher conclude from these data that there is a significant difference between the mean concentration in tablets produced at Site 1 and Site 2?What is (are) the parameter(s) we are conducting inference on? Choose one of the following symbols (m; mD(the mean difference from a matched pairs design);m1 - m2 (the mean difference from independent samples); p, or p1 - p2) and describe it in words.Depending on your answer to part (a), construct one or two histograms and one or two boxplots to visualize the distribution(s) of your sample data. If you construct two histograms and two boxplots, please construct two separate Minitab histograms (using 6 classes for Site 1's data and 7 classes for Site 2's data and cut points) and one Minitab boxplot displaying both boxes on one graph. Remember to properly title and label these graphs and use cut points for histograms. Copy and paste these graphs into your assignment. Below the graphs, answer the following questions.Are there any major deviations from normality? Are there any outliers present? Is it appropriate to conduct statistical inference procedures, why or why not?
If the answer to part iii is no, do not complete the rest of #2.
At the 0.05 significance level, can the researcher conclude from these data that there is a significant difference between the mean concentration in tablets produced at Site 1 and Site 2?
- State the null and alternative hypotheses.
- State the significance level for this problem.
- Calculate the test statistic.
- Calculate the P-value and include the probability notation statement.
- State whether you reject or do not reject the null hypothesis.
- State your conclusion in context of the problem (i.e. interpret your results).
- Construct a 95% confidence interval for the above data. Interpret this confidence interval.
In an attempt to increase business on Monday nights, a restaurant offers a free dessert with every dinner order. Before the offer, the mean number of dinner customers on Monday was 150. The numbers of diners on a random sample of 12 days while the offer was in effect are selected. Can you conclude that the mean number of diners increased while the free dessert offer was in effect?
What is (are) the parameter(s) we are conducting inference on? Choose one of the following symbols (m; mD(the mean difference from a matched pairs design);m1 - m2 (the mean difference from independent samples); p, or p1 - p2) and describe it in words.
Construct a normal probability plot and a boxplot to visualize the distribution of your sample data. Copy and paste these graphs into
- your assignment. Below the graphs, answer the following questions.
- Are there any major deviations from normality?
- Are there any outliers present?
- Is it appropriate to conduct statistical inference procedures, why or why not?
If the answer to part iii is no, do not complete the rest of #3.
At the 0.01 significance level, can you conclude that the mean number of diners increased from 150 while the free dessert offer was in effect?State the null and alternative hypotheses.State the significance level for this problem.Calculate the test statistic. Calculate the P-value and include the probability notation statement.State whether you reject or do not reject the null hypothesis.State your conclusion in context of the problem (i.e. interpret your results).Construct a 99% confidence interval for the above data. Interpret the confidence interval.
According to a report of the Nielsen Company, 65% of Internet searches used Google as the search engine. Assume that a sample of 13 searches is studied. Let the random variable be the number of searches where Google was used.
- What is the name of the probability distribution of X? Write out the setting (i.e. write out the four requirements of a particular setting that you learned in class).
- Produce a table that lists the possible values of the random variable and the corresponding probabilities of each value's occurrence.
- What is the mean of this distribution? Show work using the formula.
- What is the standard deviation of this distribution? Show work using the formula.
- Calculate the probability that of the 13 searches analyzed, at least 8 of those searches used Google. Display a Minitab Graph with the correct portion shaded as the answer to this question. Then, verify your answer with using the table you displayed in part (b).
According to the U.S. Department of Agriculture, 58.8% of males between 20 and 39 years old consume the minimum daily requirement of calcium. After an aggressive "Got milk" advertising campaign, the USDA conducted a survey of 55 randomly selected males between the ages of 20 and 39 and finds that 36 of them consume the recommended daily allowance of calcium. What is (are) the parameter(s) we are conducting inference on? Choose one of the following symbols (m; mD(the mean difference from a matched pairs design);m1 - m2 (the mean difference from independent samples); p, or p1 - p2) and describe it in words.Construct a 96% confidence interval for the above data. Interpret the confidence interval as we learned in class. Show your work using the formulas.Construct a 96% confidence interval for the above data using the Plus Four Estimate. Interpret the confidence interval as we learned in class. Show your work using the formulas.
- At the 0.05 significance level, is there evidence to conclude that the percentage of males between the ages of 20 and 39 who consume the recommended daily allowance of calcium has increased?
- State the null and alternative hypotheses.
- State the significance level for this problem.
- Check the conditions that allow you to use the test statistic, and, if appropriate, calculate the test statistic.
- Calculate the P-value and include the probability notation statement.
- State whether you reject or do not reject the null hypothesis.
- State your conclusion in context of the problem (i.e. interpret your results).
If the true population proportion was 0.588, did you commit an error? If so, which type of error did you commit and why? If not, why not? Answer in complete sentences. 1. Tocombat red-light-running crashes, many states are installing red light camerasat dangerous intersections. Thesecameras photograph the license plates of vehicles that run red lights andautomatically issue tickets. Howeffective are these photo enforcement programs? The Virginia Department of Transportation (VDOT) conducted acomprehensive study of its newly adopted program and published the results in a2012 study. In one portion of the study,VDOT provided crash data both before and after installation of the cameras atseveral intersections. The data,measured as the number of crashes caused by red light running per intersectionper year, for 13 intersections in Fairfax County are given in the first columnsin the Minitab file.
a. Whatis (are) the parameter(s) we are conducting inference on? Choose one of the following symbols (m; mD(the meandifference from a matched pairs design);m1 - m2 (the mean difference fromindependent samples); p, or p1 - p2) anddescribe it in words.
b. Dependingon your answer to part (a), construct one or two probability plots and one ortwo boxplots to visualize the distribution(s) of your sample data. If you construct two probability plots andtwo boxplots, please construct two separate Minitab probability plots and oneMinitab boxplot displaying both boxes on the same graph. Also, properly title and label your graphs. Copyand paste these graphs into your assignment. Below the graphs, answer the following questions.
i. Are there any major deviations from normality?
ii. Are there any outliers present?
iii. Is it appropriate to conduct statisticalinference procedures, why or why not?
If the answer to part iii is no, donot complete the rest of #1.
c. Atthe 0.01 significance level, test the claim that the installation of thecameras decreased the mean number of crashes at these particular intersections.
i. State the null and alternative hypotheses.
ii. State the significance level for this problem.
iii. Calculate the test statistic (subtract after -before)
iv. Calculate the P-value and include the probability notation statement.
v. State whether you reject or do not reject thenull hypothesis.
vi. State your conclusion in context of the problem(i.e. interpret your results).
d. Forthe above situation, construct a 96.2% confidence interval for the above data. Interpret the confidence interval as welearned in class.
Note: For part d, toearn full credit, show how you obtained the critical value for the confidenceinterval in Minitab. Then, write out theconfidence interval formula you would use, and the steps necessary to constructthe confidence interval.
2. Scientistscan use high-performance liquid chromatography to determine the amount of drugin a tablet. Twenty-five tablets wereproduced at each of two different sites. Drug concentrations, measured as a percentage, for the tablets producedat the two different sites are found in column C6 and C7 in the Minitab datafile. At the 0.05 significance level,can a researcher conclude from these data that there is a significantdifference between the mean concentration in tablets produced at Site 1 andSite 2?
a. Whatis (are) the parameter(s) we are conducting inference on? Choose one of the following symbols (m; mD(the meandifference from a matched pairs design);m1 - m2 (the mean difference fromindependent samples); p, or p1 - p2) anddescribe it in words.
b. Dependingon your answer to part (a), construct one or two histograms and one or twoboxplots to visualize the distribution(s) of your sample data. If you construct two histograms and twoboxplots, please construct two separate Minitab histograms (using 6 classes forSite 1's data and 7 classes for Site 2's data and cut points) and one Minitab boxplotdisplaying both boxes on one graph. Rememberto properly title and label these graphs and use cut points for histograms. Copy and paste these graphs into yourassignment. Below the graphs, answer thefollowing questions.
i. Are there any major deviations from normality?
ii. Are there any outliers present?
iii. Is it appropriate to conduct statisticalinference procedures, why or why not?
If the answer to part iii is no, donot complete the rest of #2.
c. Atthe 0.05 significance level, can the researcher conclude from these data thatthere is a significant difference between the mean concentration in tabletsproduced at Site 1 and Site 2?
i. State the null and alternative hypotheses.
ii. State the significance level for this problem.
iii. Calculate the test statistic.
iv. Calculate the P-value and include the probability notation statement.
v. State whether you reject or do not reject thenull hypothesis.
vi. State your conclusion in context of the problem(i.e. interpret your results).
d. Constructa 95% confidence interval for the above data. Interpret this confidence interval.
3. In an attempt to increase business onMonday nights, a restaurant offers a free dessert with every dinner order. Before the offer, the mean number of dinnercustomers on Monday was 150. The numbersof diners on a random sample of 12 days while the offer was in effect areselected. Can you conclude that the meannumber of diners increased while the free dessert offer was in effect?
a. Whatis (are) the parameter(s) we are conducting inference on? Choose one of the following symbols (m; mD(the meandifference from a matched pairs design);m1 - m2 (the mean difference fromindependent samples); p, or p1 - p2) anddescribe it in words.
b. Constructa normal probability plot and a boxplot to visualize the distribution of yoursample data. Copy and paste these graphsinto your assignment. Below the graphs,answer the following questions.
i. Are there any major deviations from normality?
ii. Are there any outliers present?
iii. Is it appropriate to conduct statisticalinference procedures, why or why not?
If the answer to part iii is no, donot complete the rest of #3.
c. Atthe 0.01 significance level, can youconclude that the mean number of diners increased from 150 while the freedessert offer was in effect?
i. State the null and alternative hypotheses.
ii. State the significance level for this problem.
iii. Calculate the test statistic.
iv. Calculate the P-value and include the probability notation statement.
v. State whether you reject or do not reject thenull hypothesis.
vi. State your conclusion in context of the problem(i.e. interpret your results).
d. Constructa 99% confidence interval for the above data. Interpret the confidence interval.
4. According to a report of the Nielsen Company,65% of Internet searches used Google as the search engine. Assume that a sample of 13 searches isstudied. Let the random variable bethe number of searches where Google was used.
a. Whatis the name of the probability distribution of X? Write out the setting(i.e. write out the four requirements of a particular setting that you learnedin class).
b. Producea table that lists the possible values of the random variable and the correspondingprobabilities of each value's occurrence.
c. Whatis the mean of this distribution? Showwork using the formula.
d. Whatis the standard deviation of this distribution? Show work using the formula.
e. Calculatethe probability that of the 13 searches analyzed, at least 8 of those searchesused Google. Display a Minitab Graphwith the correct portion shaded as the answer to this question. Then, verify your answer with using the tableyou displayed in part (b).
5. According to the U.S. Department ofAgriculture, 58.8% of males between 20 and 39 years old consume the minimumdaily requirement of calcium. After anaggressive "Got milk" advertising campaign, the USDA conducted a survey of 55randomly selected males between the ages of 20 and 39 and finds that 36 of themconsume the recommended daily allowance of calcium.
a. Whatis (are) the parameter(s) we are conducting inference on? Choose one of the following symbols (m; mD(the meandifference from a matched pairs design);m1 - m2 (the mean difference fromindependent samples); p, or p1 - p2) anddescribe it in words.
b. Constructa 96% confidence interval for the above data. Interpret the confidence interval as we learned in class. Show your work using the formulas.
c. Constructa 96% confidence interval for the above data using the Plus Four Estimate. Interpret the confidence interval as welearned in class. Show your work usingthe formulas.
d. Atthe 0.05 significance level, is there evidence to conclude that the percentageof males between the ages of 20 and 39 who consume the recommended dailyallowance of calcium has increased?
i. State the null and alternative hypotheses.
ii. State the significance level for this problem.
iii. Check the conditions that allow you to use thetest statistic, and, if appropriate, calculate the test statistic.
iv. Calculate the P-value and include the probability notation statement.
v. State whether you reject or do not reject thenull hypothesis.
vi. State your conclusion in context of the problem(i.e. interpret your results).
e. If the true population proportion was 0.588, didyou commit an error? If so, which typeof error did you commit and why? If not,why not? Answer in complete sentences.