STATS 302 EXAM 2 HW 8

A consumer advocate agency is concerned about reported failures of two brands of mp3 players, brand a and b. In a random sample of 197 brand a players, 33 units failed within 1 year of purchase. Of the 290 Brand B players, 25 units were reported to have failed within the first year. The agency is interested in the difference between the population proportions pa-pb for the two brands What is the 99% confidence interval estimate of the true difference?

(0.0007, 0.1619)

Airline companies are interested in the consistency of the number of babies on each flight, so that they have adequate safety equipment. Suppose an airline conducts a survey. Over Thanksgiving weekend, it surveys fix flights from from Boston to Salt Lake City to determine the number of babies on the flights. It determines the amount of safety equipment needed by the result of that study. Select the things that were wrong with the way the survey was conducted.

- The survey was conducted using six similar flights - Conducting the survey on a holidy weekend will not produce representative results - The survey would not be a true representation of the entire population of air travelers

A psychologist wants to know if the difficulty of a task influcences our estimate of how long we spend working on it. She designs two sets of mazes that subjects can work through a computer. One set has easy mazes and the other has hard mazes. Subjects work until told to stop. They are asked to estimate how long they worked. 30 subjets Describe the design of a completely randomized experiment to learn the effect of difficulty on estimated time

-Compare the time estimates of Group 1 and 2 - Randomly assign 15 students to Group 1 and other 15 to Group 2

Airline companies are interested in the consistency of the number of babies on each flight, so that they have adequate safety equipment. Suppose an airline conducts a survey. Over Thanksgiving weekend, it surveys fix flights from from Boston to Salt Lake City to determine the number of babies on the flights. It determines the amount of safety equipment needed by the result of that study. Select the ways you would improve the survey if it were to be repeated

-Conduct the survey on different days of the week - Conduct the survey using flights to and from various locations - Conduct the survey during different times of the year

A psychologist wants to know if the difficulty of a task influcences our estimate of how long we spend working on it. She designs two sets of mazes that subjects can work through a computer. One set has easy mazes and the other has hard mazes. Subjects work until told to stop. They are asked to estimate how long they worked. 30 subjets Describe how the design of a matched pairs experiment using the same 30 subjects

-Each student does the activity twice, once with easy mazes and the other time with hard mazes. - Randomly decide which set of mazes is used first - Compare each students "easy" and "hard" time estimates

A consumer advocate agency is concerned about reported failures of two brands of mp3 players, brand a and b. In a random sample of 197 brand a players, 33 units failed within 1 year of purchase. Of the 290 Brand B players, 25 units were reported to have failed within the first year. The agency is interested in the difference between the population proportions pa-pb for the two brands IF it were believed that the two population proportions were actually eual, what would be the standard error of estimated difference?

0.0299

The national Health Interview Survey conducted of 33,326 adults by the US national center for health statistics in 2003 indicated that 21.4% of adults were current smokers. A similar study conducted in 1991 of 42,000 adults indicated that 25.6% were current smokers. (1=1991 and 2=2003) Find a point estimate of the difference between the proportion of current smokers in 1991 and current smokers in 2003.

0.042

A recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national percent. Suppose that a survey of 100 local seniors and 100 national seniors is conducted to see if the proportion of drug and alcohol use is higher locally than nationally. Locally 69 seniors reported using drugs or alcohol while 60 national seniors reported using them. Conduct a hypothesis test at the 5% level of significance. What is the p-value?

0.0918

The Diabetes Control and complications trial followed by diabetes patients diagnosed with retinopathy before joining the study. They were randomly assigned to one of two treatments and monitored for 6 years. The study found that 155 of the 345 patients assigned to the conventional treatment showed a sustained progression of their original retinopathy. In contrast, only 82 of the 359 patients assigned to the intensive treatment had sustained retinopathy progression Find a point estimate of the difference between the proportion of conventional treatment patients with sustained retinopathy progression and the proportion of intensive treatment patients

0.221

A recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national percent. Suppose that a survey of 100 local seniors and 100 national seniors is conducted to see if the proportion of drug and alcohol use is higher locally than nationally. Locally 69 seniors reported using drugs or alcohol while 60 national seniors reported using them. Conduct a hypothesis test at the 5% level of significance. Indicate the correct decision 1. Alpha 2. Decision 3. Reason 4. conlcusion

1. 0.05 2. Do not reject the null hypothesis 3. Since p-value >a, we do not reject the null hypothesis 4. There is not sufficient evidence to show that the proportion of local seniors using drugs and alcohol locally is higher than the proportion of seniors using nationally

There have been anecdotal reports of the ability of duct tape to remove warts. In an experiment conducted at the Madigan Army Medical Center in the state of Washington, 51 patients between the ages 3 and 22 were randomly assigned to receive either duct tape therapy or cryotherapy. After 2 months, the percentage successfully treated was 85% in the duct tape group and 60% in the cryotherapy group. 1.Explanatory Variable 2. Experimental units 3. Treatments 4. Response variable

1. Type of treatment for removing warts 2. 51 subjects between 3 and 22 3. Duct tape or cryotherapy 4. Whether the wart was successfully removed

Ability to grow in shade may help pines found in the dry forests of Arizona resist drought. How well do these pines grow in shade? Full light, light reduced to 25% of normal by shade cloth or light reduced to 5% of normal. As the end of the study, they dried the young trees and weighed them. 1.Response Variable 2. Treatments 3. Explanatory variable 4. Individuals

1. Weight 2. type of Light 3. amount of light 4. pines

The U.S. Center for diesease control reports that the mean life expectancy was 47.6 years for whites fron in 1900 and 33 years for non whites. Suppose that u randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the mean life span as 45.3 years with a standard deviation of 12.7 years. Of the 82 nonwhites, the mean life span as 34.1 years with a standard deviation of 15.6 years. Conduct a hypothesis test The standard error of (x(w)-x(nw)) equals

2.066

Aspirin prevents blood from clotting and helps prevent strokes. The Second European Stroke Prevention Study asked whether adding another anti-clotting drug named dipyridamole would be more effective for patients who already had a stroke. What is the test statistic ? p-value?

2.98 0.0029

Which of the following statements is correct for the paired t test?

A paired t test is a one sample t test on the differences of the observations in the two groups

When should a paired t test be performed instead of a two sample t test?

A paired t test should be performed instead of two sample t tests when each observation in one group has a dependence on a particular observation in the other group

The Diabetes Control and complications trial followed by diabetes patients diagnosed with retinopathy before joining the study. They were randomly assigned to one of two treatments and monitored for 6 years. The study found that 155 of the 345 patients assigned to the conventional treatment showed a sustained progression of their original retinopathy. In contrast, only 82 of the 359 patients assigned to the intensive treatment had sustained retinopathy progression A 95% confidence interval for the difference in the two proportions, p1-p2, is (.153,.289). What does this mean?

Because the interval does not contain 0, there is enough evidence at the 0.05 level to conclude that the two proportions are significantly different

A large medical experiment assigned 1649 women to take either strontium renelate or a placebo everyday. All of the subjects had osteoporosis and suffered at least 1 fracture. All were taking calcium supplements and receiving standard medical care. The response variables were measurements of bone density and counts of new fractures over 3 years. The subjects were treated at 10 medical centers in 10 countries. Outline a block design for this experiment, with the medical centers as blocks.

Blocking by medical center means that we randomly assing half of the women from country A to the strontium renelate group, along with half the women in country b and so on

Can changing diet reduce high blood pressure? Vegetarian diets and low salt diets are both promising. The 240 subjects are labeled 001 to 240. Software assigns an SRS of 60 subjects to diet 1 and so on. What is the response variable

Change in blood pressure after 8 weeks on assigned diet

One major reason that the two sample t procedures are widely used is that they are quite robust. What does this mean?

Confidence levels and p-values from the t procedures are quite accurate even if the population distriubtion is not exactly normal

A consumer advocate agency is concerned about reported failures of two brands of mp3 players, brand a and b. In a random sample of 197 brand a players, 33 units failed within 1 year of purchase. Of the 290 Brand B players, 25 units were reported to have failed within the first year. The agency is interested in the difference between the population proportions pa-pb for the two brands From these date, the point estimate of the true difference between the proportions and the standard error or estimate are

D= 0.0813 SEd= 0.0313

The most common treatment for breast cancer discovered in its early stages was once removal of the breast. It is now usual to remove only the tumor and nearby lymph nodes, followed by radiation. To study whether these treatments differ in their effectiveness, a medical team examines the records of 25 large hospitals and compares the survival times after surgery of all women who have had either treatment. Explain why confounding will prevent this study from discovering which treatment is more effective.

Doctors may decide which treatment to recommend based in part on how advanced the case is.

The most common treatment for breast cancer discovered in its early stages was once removal of the breast. It is now usual to remove only the tumor and nearby lymph nodes, followed by radiation. To study whether these treatments differ in their effectiveness, a medical team examines the records of 25 large hospitals and compares the survival times after surgery of all women who have had either treatment. What are the explanatory and response variables?

E: treatment method R: survival times

Ability to grow in shade may help pines found in the dry forests of Arizona resist drought. How well do these pines grow in shade? Full light, light reduced to 25% of normal by shade cloth or light reduced to 5% of normal. As the end of the study, they dried the young trees and weighed them. What type of study is this?

Experiment: completely randomized design

The commuity Intervention Trial for Smoking Cessation asked whether a community wide advertising campaign would reduce smoking. The researchers located 11 pairs of communities for which the members of each pair were similar in location, size, economic status and so on. One community in each pair was randomly selected to participate and the other was not. What type of study is this?

Experiment: matched pairs design

An ultramarathon is a footrace longer than 26.2 miles of a marathon. Will is taking 600 mg of vitamin C daily to reduce these infetions. Researchers randomly assigned runners to receive either vitamin c or a placebo. They also assigned these treatments to non runners. All subjects were watched for 14 days after the big race to see if infections developed. What type of study is this?

Experiment: randomized block design

Aspirin prevents blood from clotting and helps prevent strokes. The Second European Stroke Prevention Study asked whether adding another anti-clotting drug named dipyridamole would be more effective for patients who already had a stroke. The hypothesis to be tested are

H0: p1=p2 vs Ha: p1=/ p2

A recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national percent. Suppose that a survey of 100 local seniors and 100 national seniors is conducted to see if the proportion of drug and alcohol use is higher locally than nationally. Locally 69 seniors reported using drugs or alcohol while 60 national seniors reported using them. Conduct a hypothesis test at the 5% level of significance. State the null hypothesis

H0: plocal=pnational

A recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national percent. Suppose that a survey of 100 local seniors and 100 national seniors is conducted to see if the proportion of drug and alcohol use is higher locally than nationally. Locally 69 seniors reported using drugs or alcohol while 60 national seniors reported using them. Conduct a hypothesis test at the 5% level of significance. State the alternative hypothesis

Ha: plocal>pnational

The U.S. Center for diesease control reports that the mean life expectancy was 47.6 years for whites fron in 1900 and 33 years for non whites. Suppose that u randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the mean life span as 45.3 years with a standard deviation of 12.7 years. Of the 82 nonwhites, the mean life span as 34.1 years with a standard deviation of 15.6 years. Conduct a hypothesis test State the null and alternative hypothesis

Ho: uw=unw Ha: uw=/unw

A recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national percent. Suppose that a survey of 100 local seniors and 100 national seniors is conducted to see if the proportion of drug and alcohol use is higher locally than nationally. Locally 69 seniors reported using drugs or alcohol while 60 national seniors reported using them. Conduct a hypothesis test at the 5% level of significance. Expalin what the p-value means for this problem.

If Ho is ture, then there is a chance equal to the p-value that the proportion of students who use drugs and alcohol locally is at least 0.09 more than the proportion of students who use nationally

A sociologist wants to test the theory that the number of serious relationships that men and women have before age 21 is different. She takes a SRS of 45 women and a SRS of 50 men between 21 and 25. The researcher determines the number of serious relationships each individual in her study had befroe the age of 21. Which test and hypothesis are appropriate

Independent Samples T test Ho: umen-uwomen=0 and Ha: umen-uwomen=/ 0

A study in El Paso, Texas, looked at seat belt use by drivers. Drivers were observed at randomly chosen convenience stores. After they left their cars, they were invited to answer questions that included questions about seat belt use. In all, 75% said they always used seat belts, yet only 61.5% were wearing seat belts when they pulled into the store. Explain the reason for the bias observed in responses to the survery

It is response bias due to the negative perception of not using a seatbelt

A study aims to evaluate the percent of adults whose right cerebral hemisphere is larger than their left hemisphere. A group of individuals aged 20 and older representative of the American adult population is asked to come to a brain-imaging facility to have their brains scanned. Each individual's scan is then analyzed to identify whether the right or left cerebral hemisphere is larger. What is the variable of interest?

Larger hemisphere (left, right)

To select a sample of undergraduate students in the United States, you select a simple random sample of four states. From each of these states, you select a simple random of 2 colleges or universities. Finally, from each of these 8 colleges or universities, you select a simple random sample of 20 undergraduates. Your final sample consists of 160 undergraduates. What type of sampling was used?

Multistage sampling

The most common treatment for breast cancer discovered in its early stages was once removal of the breast. It is now usual to remove only the tumor and nearby lymph nodes, followed by radiation. To study whether these treatments differ in their effectiveness, a medical team examines the records of 25 large hospitals and compares the survival times after surgery of all women who have had either treatment. Explain carefully why this study is not an experiment

No treatment is actively imposed. The women ( or their doctors) chose which treatment to use.

The U.S. Center for diesease control reports that the mean life expectancy was 47.6 years for whites fron in 1900 and 33 years for non whites. Suppose that u randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the mean life span as 45.3 years with a standard deviation of 12.7 years. Of the 82 nonwhites, the mean life span as 34.1 years with a standard deviation of 15.6 years. Conduct a hypothesis test The p-value is almost 0 for this test. Does it appear that the means are the same? why or why not?

No, the means appear to be different because the hypothesis test has a p-value less than 0.05.

A study aims to evaluate the percent of adults whose right cerebral hemisphere is larger than their left hemisphere. A group of individuals aged 20 and older representative of the American adult population is asked to come to a brain-imaging facility to have their brains scanned. Each individual's scan is then analyzed to identify whether the right or left cerebral hemisphere is larger. What type of study is this?

Observation study: cross-sectional (bcs it gathers data from the present time)

Many studies have found that people who drink alcohol in moderation have lower risk of heart attacks than either nondrinkers or heavy drinkers. Does alcohol consumption also improve survival after a heart attack? One study followed 1913 people who were hospitalized after severe heart attacks. In the year before their heart attacks, 47% of these people did not drink, 36% drank moderately and 17% drank heavily. After 4 years, fewer of the moderate drinkers had died. What type of study is this?

Observational study: prospective (bcs subjects are followed 4 years into the future)

A study of cell phones and the risk of brain cancer looked at a group of 469 people who had brain cancer. The investigators matched each cancer patient with a person same sex, age, and race who did not have brain cancer. Result: "Our data suggest that use of handheld cellular telephones is not associated with risk of brain cancer." What type of study is this?

Observational study: retrospective

Among a group of disabled women aged 65 and older who were tracked for several years, those who had a vitamin b12 deficiency were twice as likely to suffer severe depression as those who did not What type of study is this?

Observational: prospective

Genetic influences on cancer can be studied by manipulating the genetic makeup of mice. one of the processes that turn genes on and off in locations is dna methylation. do low levels of this process help cause tumors? Of 32 mice with lowered methylation, 20 developed tumores. None of the control group of 19 normal mice developed tumors in the same time period Explain why we cannot safely use either the large sample confidence interval or the test for comparing the proportions of normal and altered mice that develop tumors

One of the counts is 0. For large sample intervals, all counts must be at least 10, and for significant testing, all counts must be at least 5.

Anna's project for her introductoy statistics course was to compare the selling prices of textbooks at two internet bookstores. she first took a random sample of ten textbooks used that term in courses at her college, based on the list of texts compiled by college bookstore. Then she obtained prices of the 10 randomly selected textbooks at the two internet sites to test if the average prices of textbooks sold at the two internet bookstoes are different Which test and hypothesis is appropriate

Paired T Teset H0: ud=0 and Ha: ud=/0 where ud=mean difference in textbook prices

Researchers studied a group of 10982 middle aged adults over a period of nine years. They found that smokers who quit had a higher risk for diabetes within three years of quitting than either nonsmokers or continuing smokers. Does this show that stopping smoking causes the short-term risk for diabetes to increase? (Weight gain has been shown to be a major risk in developing type 2 diabetes and is often a side effect of quitting smoking) Based on this research, should you tell a middle aged adult who smokes that stopping smoking can cause diabetes and advise him or her to continue smoking?

Since this is an observational study, it is not reasonable to conclude any cause-and-effect relationships. At best, we might advise smokers that they should be mindful of potential weight gain.

Among a group of disabled women aged 65 and older who were tracked for several years, those who had a vitamin b12 deficiency were twice as likely to suffer severe depression as those who did not What is the parameter of interest if observation or response if experimental?

Suffering sever depression

The U.S. Center for diesease control reports that the mean life expectancy was 47.6 years for whites fron in 1900 and 33 years for non whites. Suppose that u randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the mean life span as 45.3 years with a standard deviation of 12.7 years. Of the 82 nonwhites, the mean life span as 34.1 years with a standard deviation of 15.6 years. Conduct a hypothesis test IF you were to construct a 95% confidence interval to estimate uw-unw, which one of the following about this confidence is true?

The confidence interval wouldn't contain 0 bcause the p-value is less than 0.05.

Can changing diet reduce high blood pressure? Vegetarian diets and low salt diets are both promising. The 240 subjects are labeled 001 to 240. Software assigns an SRS of 60 subjects to diet 1 and so on. What are the explanatory variables in the experiment?

There are two: diet (normal, vegetarian) and salt (restricted, unrestricted)

The national Health Interview Survey conducted of 33,326 adults by the US national center for health statistics in 2003 indicated that 21.4% of adults were current smokers. A similar study conducted in 1991 of 42,000 adults indicated that 25.6% were current smokers. (1=1991 and 2=2003) A 99% confidence interval for the difference in the two proportions, p1-p2, is (0.034, 0.050). What does this mean?

There is evidence of a decline in current smokers between 1991 and 2003.

Aspirin prevents blood from clotting and helps prevent strokes. The Second European Stroke Prevention Study asked whether adding another anti-clotting drug named dipyridamole would be more effective for patients who already had a stroke. What is the conclusion at the a=0.05 significance level?

There is sufficient evidence at the 0.05 level that the proportion of strokes is different for the two groups.

A large medical experiment assigned 1649 women to take either strontium renelate or a placebo everyday. All of the subjects had osteoporosis and suffered at least 1 fracture. All were taking calcium supplements and receiving standard medical care. The response variables were measurements of bone density and counts of new fractures over 3 years. The subjects were treated at 10 medical centers in 10 countries. Explain why this is the proper design

This block design would control for any differences in the level of medical care from one country to another

A study in El Paso, Texas, looked at seat belt use by drivers. Drivers were observed at randomly chosen convenience stores. After they left their cars, they were invited to answer questions that included questions about seat belt use. In all, 75% said they always used seat belts, yet only 61.5% were wearing seat belts when they pulled into the store. Do you expect bias in the same direction in most surveys about seat belt use?

Yes, such bias is likely in most surveys about seat belt use (and similar topics)

Many studies have found that people who drink alcohol in moderation have lower risk of heart attacks than either nondrinkers or heavy drinkers. Does alcohol consumption also improve survival after a heart attack? One study followed 1913 people who were hospitalized after severe heart attacks. In the year before their heart attacks, 47% of these people did not drink, 36% drank moderately and 17% drank heavily. After 4 years, fewer of the moderate drinkers had died. What is the explanatory variablw?

alcohol consumption level (none,moderate,heavy)

Many studies have found that people who drink alcohol in moderation have lower risk of heart attacks than either nondrinkers or heavy drinkers. Does alcohol consumption also improve survival after a heart attack? One study followed 1913 people who were hospitalized after severe heart attacks. In the year before their heart attacks, 47% of these people did not drink, 36% drank moderately and 17% drank heavily. After 4 years, fewer of the moderate drinkers had died. What populations are represented in the study?

all individuals who have suffered a severe heart attack

An experiment that claimed to show that meditation reduces anxiety proceeded as follows. The experimenter interviewed the subjects and rated their level of anxiety. Then the subjects were randomly assigned to two groups. The experimenter taught one group how to meditate and they did daily for month. The other group was told to relax more. The meditation group had less anxiety after a month. What property of good experiments is missing from the study?

blinding

A study of cell phones and the risk of brain cancer looked at a group of 469 people who had brain cancer. The investigators matched each cancer patient with a person same sex, age, and race who did not have brain cancer. Result: "Our data suggest that use of handheld cellular telephones is not associated with risk of brain cancer." What is the response variable?

brain cancer

A study of cell phones and the risk of brain cancer looked at a group of 469 people who had brain cancer. The investigators matched each cancer patient with a person same sex, age, and race who did not have brain cancer. Result: "Our data suggest that use of handheld cellular telephones is not associated with risk of brain cancer." What is the explanatory variable?

cell phone usage

Can changing diet reduce high blood pressure? Vegetarian diets and low salt diets are both promising. The 240 subjects are labeled 001 to 240. Software assigns an SRS of 60 subjects to diet 1 and so on. This is an example of which of the following?

completely randomized design

Many studies have found that people who drink alcohol in moderation have lower risk of heart attacks than either nondrinkers or heavy drinkers. Does alcohol consumption also improve survival after a heart attack? One study followed 1913 people who were hospitalized after severe heart attacks. In the year before their heart attacks, 47% of these people did not drink, 36% drank moderately and 17% drank heavily. After 4 years, fewer of the moderate drinkers had died. What is the response variable?

death (yes,no)

A researcher wants to compare the effect of a new type of shampoo on hair condition. The researcher believes that men and women may react to the shampoo differently. Additionally, the researcher believes that the shampoo will react differently on hair that is dyed. The subjects are split into four groups: men who dye their hair, men who dont, women who do and women who dont. Subjects in each group are randomly assigned to the new shampoo and old shampoo. This experiment....

has one factor (shampoo type), blocked by gender and whether hair is dyed

A recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national percent. Suppose that a survey of 100 local seniors and 100 national seniors is conducted to see if the proportion of drug and alcohol use is higher locally than nationally. Locally 69 seniors reported using drugs or alcohol while 60 national seniors reported using them. Conduct a hypothesis test at the 5% level of significance. In words, state what your random variable p(hat)local-p(hat)national represents

p(hat)local-p(hat)national represents the difference in sample proportions of drug and alcohol abuse of local and national seniors

An ultramarathon is a footrace longer than 26.2 miles of a marathon. Will is taking 600 mg of vitamin C daily to reduce these infetions. Researchers randomly assigned runners to receive either vitamin c or a placebo. They also assigned these treatments to non runners. All subjects were watched for 14 days after the big race to see if infections developed. What is the response variable?

respiratory infection

Can changing diet reduce high blood pressure? Vegetarian diets and low salt diets are both promising. The 240 subjects are labeled 001 to 240. Software assigns an SRS of 60 subjects to diet 1 and so on. The FDA should be reluctant to use the results of the experiment describes above for its guideline on diets for Americans with high blood pressure bcs

results from men with high blood prssure may not generalize the population of all Americans with high blood pressure (male/female)

An ultramarathon is a footrace longer than 26.2 miles of a marathon. Will is taking 600 mg of vitamin C daily to reduce these infetions. Researchers randomly assigned runners to receive either vitamin c or a placebo. They also assigned these treatments to non runners. All subjects were watched for 14 days after the big race to see if infections developed. What are the explantory variables

runner (yes,no) Vitamin C (yes no)

Randomization in an experiment is important because it ensures that

the groups of subjects are similar, on average, in all resects before applying different treatments to different groups

The U.S. Center for diesease control reports that the mean life expectancy was 47.6 years for whites fron in 1900 and 33 years for non whites. Suppose that u randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the mean life span as 45.3 years with a standard deviation of 12.7 years. Of the 82 nonwhites, the mean life span as 34.1 years with a standard deviation of 15.6 years. Conduct a hypothesis test In symbols, what is the random variable of itnerest for this test?

x(w)-x(nw)

A recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national percent. Suppose that a survey of 100 local seniors and 100 national seniors is conducted to see if the proportion of drug and alcohol use is higher locally than nationally. Locally 69 seniors reported using drugs or alcohol while 60 national seniors reported using them. Conduct a hypothesis test at the 5% level of significance. What is the test statistic?

z= 1.33