Statistics Test Four Review

Living with parents: a pew research analysis stated that in 2012, 36% of the nations young adults ages 18 to 31 (the so-called millennial generation) were living in their parents home. After reading the analysis, a statistics student wanted to design a study to determine if the percentage was higher for the millennial students what attended his college. Before collecting data, he said the significance level for his test to be 0.05. For which P value would he reject the no hypothesis?

0.02

The tire manufacturer has 60,000 miles warranty for a tread life. The manufacturer considers the overall tire quality to be acceptable if less than 5% of one out at 60,000 miles. The manufacture test 250 tires that have been used for 60,000 miles. They find that none of them are worn out. But this data, it has the following hypotheses at the 5% significance level. The P - value is 0.15. H_0: the proportion of tires that are worn out after 60,000 miles is equal to 0.05 H_a: the proportion of tires that are worn out after 60,000 miles is less than 0.5. Which of the following conclusions is correct?

Fail to reject H_zero We never ever ever except H

A researcher took a random sample of 100 students from a large university. She computed a 95% confidence interval to estimate the average weight of the students at this university. The confidence interval was too wide to provide a precise estimate. True or false? The researcher could produce a narrower confidence interval by increasing the sample size to 150.

False

A quality control engineer at a potato chip company test the bag filling machine 5 AM bags of potato chips. Not every bag contains exactly the same weight. That is more than 11% of bags are overfilled then they stopped production to fix the machine. Need to find overfilled to be more than 1 ounce above the weight on the package. The engineer weighs 106 bags and find that 30 of them are overfilled. He plans to test the hypothesis H_0: P equals 0.11 versus H_a: P > 0.11. What is the test statistic?

H_0: p = H_a: p = Phat N St. Error - sqrt(p_0*(1-p_0)/n) Z - standardize(phat,p_0,st. Error) P-value - <: norm.dist(Z,0,1,1) - left tailed >: 1-norm.dist(Z,0,1,1) - right tailed ≠: 2*(1-norm.dist(abs(Z),0,1,1)) - two tailed test

In 2016 the centers for disease control reported that the team birth rate in Georgia is 23.8%. The Atlanta city council what is a study to see if the team birth rate within the city of Atlanta is lower. Suppose that a study of 1000 female teenagers in Atlanta found that 234 of them gave birth in 2016. Given that the population proportion is understood to be P equals 0.238, what would be the null hypothesis, H_0, for the study?

H_O: P < 23.8%

Genetically modified foods: According to 2016, pew research survey, a majority of the American general public (56%) says that genetically modified foods are generally unsafe to eat. This month, and a survey of 500 randomly selected American adults, 58% says that genetically modified foods are generally unsafe to eat. We test the hypothesis that the percentage who says that genetically modified foods are generally unsafe to eat, is greater than 56% this year. The P - value is 0.089. Which of the following interpretations of this P - value is valid?

If we assume that 56% of Americans say that genetically modified foods are generally unsafe to eat, then there is a 8.9% chance that a random sample results will show 58% or more who say that genetically modified foods are generally unsafe to eat.

Living with parents: The Pew Research Center reported that 36% of American Millennials (adults ages 18-31) still live at home with their parents. A group of students wants to conduct a study to determine whether this result is true for students at their campus. They survey 300 randomly selected students at their campus and determine that 43% of them still live at home with their parents. With this data, they test the following hypotheses. H_0: off millennial students at the Campus, 36% live at home with their parents. H_A: more than 36% of millennial students at the Campus live at home with their parents. In order to assess the evidence, which question best describes what we need to determine?

If we examine the proportion of students at the Campus, who still lives at home with their parents, how likely is that proportion to be more than 36%?

Supposed to take a random sample of 41 State College students. Then we measure the length of their right foot in centimeters. We compute and 95% confidence interval for the mean foot length for students at this college. We get (21.71, 25.09). Suppose that we now compute and 90% confidence interval. As confidence level decreases the interval width ___.

Increases

In 2010, polls indicated that 76% of Americans favored mandatory testing for students in public schools as a way to read the school. This year and a poll of 1000 Americans 71% favor mandatory testing for this purpose. Has public opinion changed since 2010? Test of a hypothesis that the percentage supporting mandatory testing is less than 76% this year. The P - value is 0.016. Which of the following interpretation of this P - value is valid?

Is 76% of Americans still favor mandatory testing this year, then there is a 1.6% chance that the poll results will show 71% or fewer with this opinion.

Living with parents: the pew research center reported that 36% of American millennials (adults ages, 1831) still live at home with their parents. A group of students wants to conduct a study to determine whether this result is true for students at their campus. They survey 300 randomly selected students at their campus and determined that 43% of them still live at home with their parents. With this data, they test the following hypotheses at the 5% significance level. The P value is 0.006. H_0: of millennial students at the Campus, 36% live at home with their parents. H_A: more than 36% of millennial students at the campus lives at home with their parents. Which of the following conclusions is correct?

Reject H_zero

Two different groups in a statistics class are conducting a survey to estimate the main number of units. Students at their college are enrolled in. The population mean and standard deviation are unknown. The sample from the first skip survey has 49 data values. The sample from the second group survey has 81 that values. For each sample, the groups constructs, and 90% confidence interval to estimate the population mean. Which confidence interval will have a greater precision (smaller width) for estimating the population mean?

The confidence interval, based on the sample of 81 data values will be more precise.

Living with parents: the pew research center reported that 36% of American millennials still live at home with their parents. A group of students wants to conduct a study. Set a timer whether this result is true for students of the campus. They serve a 300 randomly selected students at the campus and determined that 43% of them still live at home with their parents. With this data, they test the following hypotheses at the 5% significance level. The P value is 0.006. H_0: of millennial students at the Campus, 36% live at home with their parents. H_A: more than 36% of millennial students at the Campus live at home with their parents. What can we conclude?

The evidence suggests that more than 36% of students at the campus, never home with their parents, because the P value is less than the significance level.

We conduct a study to determine whether the majority of community college student Panther vote in the next presidential election. Which is the significance level of 0.05. The service 650 randomly selected community college students and find that 54% of them front of it. The P - value is 0.02. H_0:50% of community college student, pensive boat and the next presidential election H_A: more than 50% of community college, students plentiful in the next presidential election. What can we conclude?

The evidence suggests that the majority of community college student center fell in the next presidential election, because the P - value is less than the significance level.

The makers of mini oats cereal have an automated packaging machine that is set to fill boxes with 26.1 ounces of cereal (as labeled on the box). At various times in packaging process, we select a random sample of 100 boxes to see if the machine is. (on average) filling the boxes as labeled. On Tuesday morning, at 7:45 AM, a random sample of 100 boxes please an average amount of 23.5 ounces. Which of the following is an appropriate statement of the null hypothesis?

The machine fills the boxes with the proper amount of cereal. The average is 24.1 ounces. (H_0:(Mu) = 24.1)

Living with parents: the pew research analysis stated that in 2012, 36.4% of the nations young adults ages, 18-31 (the so-called millennial generation) were living in their parents home. After reading the analysis, statistics student wanted to design a study to determine if the percentage was hired for a millennial students to attend his college. Which of the following is an appropriate statement for the null hypothesis?

The percentage of millennial students at his college, who live in their parents, home is not the same as the percentage of millennials nationwide. Example H_0: P = 36.4%

A doctor is measuring that means systolic blood pressure, a female students at a large college systolic. Blood pressure is known to have a skewed distribution. The doctor collects systolic blood pressure measurements from a random sample of 28 female students. The resulting 90% confidence interval is (100.4, 159.6) units of systolic blood pressure mmHg. which one of the following conclusions is valid?

The sampling distribution of means will probably not follow a normal distribution, so we cannot draw a conclusion.

Pregnancy testing: a college student hasn't been feeling well and visits for Campus health center. Based on her symptoms, the doctor suspects that she is pregnant and order is a pregnancy test. The results of this test could be considered a hypothesis test with the following hypotheses: h_0: the student is not pregnant. H_A: the student is pregnant. Based on the hypotheses above, which of the following statements is considered a type one error?

The student is not pregnant, but the test results shows she is pregnant

Pregnancy test 10: a college student hasn't been feeling well and physics, her campus health center. Based on her symptoms, The Doctor, suspects that she is pregnant and orders a pregnancy test. Results of this test could be considered a hypothesis test with the following hypotheses: h_0: the students is not pregnant. H_A: the student is pregnant. Based on the hypotheses above, which of the following statements is considered a type two error?

The student is pregnant, but the test results show she is not pregnant.

2014 study by the reputable Gallup organization estimates that 44% of US adults are underemployed. Underemployed means a person wants to work full-time what is important part time or unemployed. Do you want to know if the proportion of smaller this year. We select a random sample of 100 US adults this year and find that 40% of underemployed. After carrying out the hypothesis test for P equals 0.44 compared to P < 0.44 we obtain a P value of 0.21. Which of the following interpretations of the P value is correct?

There is a 21% chance that a sample of 100 US adults will have 40% off your underemployed if 44% of the population is underemployed this year

Food, inspectors inspect samples of food prep products to see if they are safe. This can be thought of as a hypothesis test but the following hypothesis. h_0: the food is safe. H_A: the food is not safe. Based on the hypotheses above, is the following statements a type one or type two error? The sample suggests that the food is not safe, but it actually is safe.

Type one

Food, inspectors inspect samples of food products to see if they are safe. This can be thought of as a hypothesis test with the following hypotheses. h_0: the food is safe. H_A: the food is not safe Based on the hypotheses above, is the following statements a type one or type two error? The sample suggest that the food is safe, but it is actually not safe.

Type two

Is smoking during pregnancy associated with premature birth? To investigate this question, researchers selected a random sample of 113 pregnant women who were smokers. The average pregnancy length for the sample of smokers was 265 days. From a large body of research, it is known that the length of human pregnancy has a standard deviation of 13 days. The researchers assume that smoking does not affect the variability in pregnancy length. Find the 99% confidence interval to estimate the length of pregnancy for women who smoke.

Xbar - 265 Sigma - 13 N - 113 CL - 0. 99. Z - 1.645(90%), 1.96(95%), 2.576(99%) SE - sigma/sqrt(n) MOE - z*SE Lower - xbar - moe Upper - xbar + moe

"About 25% of college students support academic consequences of their drinking, including missing class falling behind doing poorly on exams or papers and receiving lower grades overall." A statistics student is curious about drinking habits of students at his college. He wants to estimate the mean number of alcoholic drinks consumed each week by students at his college. He plans to use a 90% confidence interval. He surveys a random sample of 61 students. The sample mean is 3.7 alcoholic drinks per week. The sample standard deviation is 2.6 drinks. Construct the 90% confidence interval to estimate the average number of alcoholic drinks consumes each week by students at this college.

Xbar - 3.7 S - 2.6 N - 61 CL - 0.90 T - t.inc.2t(1-CL,N-1) SE - s/sqrt(n) MOE - t*SE Lower - xbar - moe Upper - xbar + moe

Estimating mean SAT math score The SAT is the most widely used college admission exam. (Most community college do not require students to take this exam). The mean SAT math score of varies by state and by year, so the value of Mu depends on the state and year. But let's assume that the shape and spread of the distribution of individual SAT math scores in each state is the same each year. More specifically, assume the individual SAT math scores consistently have a normal distribution with a standard deviation of 99. An educational researcher wants to estimate the mean SAT math score (Mu) for his state this year. The researcher chooses a random sample of 687 exams in his state. The sample mean for the test is 483. Find the 95% confidence interval estimate the mean SAT math score in the state for this year Let's use the unrounded values in excel to find the answers.

Xbar - 483 Sigma - 90 N - 687 CL - 0. 95. Z - 1.645(90%), 1.96(95%), 2.576(99%) SE - sigma/sqrt(n) MOE - z*SE Lower - xbar - moe Upper - xbar + moe

Statistics class is estimating the main heights of all female students at their college. They collect a random sample of 41 female students and measure their heights. The mean of the sample is 65.2 inches and the sample standard deviation is 5.1 inches. Find the 95% confidence interval for the main height of all female students in their school. Assume that the distribution of individual female heights at the school is approximately normal.

Xbar - 65.2 S - 5.1 N - 41 CL - 0.95 T - t.inc.2t(1-CL,N-1) SE - s/sqrt(n) MOE - t*SE Lower - xbar - moe Upper - xbar + moe

A group of engineers developed a new design for steel cable. They need to estimate the amount of weight the cable can hold. The weight limit will be reported on cable package in. The engineers take a random sample of 37 cables and apply weights to each of them until they break. The 37 cables have a mean breaking weight of 77.5.3 pounds. The standard deviation of the breaking wait for the sample is 15.3 pounds. Find the 99% confidence interval to estimate the mean breaking weight for this type of cable.

Xbar - 775.3 S - 15.3 N - 37 CL - 0.99 T - t.inc.2t(1-CL,N-1) SE - s/sqrt(n) MOE - t*SE Lower - xbar - moe Upper - xbar + moe

College students in STDs: recent report estimated that 25% of all college students in the United States, have a sexually transmitted disease. Due to the demographics of the community, the Director of Campus health center leave that the proportion of students who have STD is a lower at his college. She test H_0: P equals 0.25 versus H_A: P. < 0.25. The Campus health center stuff Celexa, random sample of 50 students and determined that 18% have been diagnosed with an STD. Is the sample size condition for conducting a hypothesis test for a population proportion satisfied?

Yes, because (50) (0.25) and (50) (1-0.25) are both at least 10. This means we can use the normal distribution to model the distribution of sample proportions.

Cording to the national Institute on drug abuse, a US government agency, 17.3% of its graders in 2010 how do use marijuana at some point in their lives. A school official hopes to show the percentage is lower in his district, testing H_0: P equals 0.173 versus H_a: P < 0.173. The health department for the district uses anonymous, random sampling, and finds that 10% of 80 eighth graders surveyed. How do use marijuana. Is the sample size condition for conducting a hypothesis test for a population proportion satisfied?

Yes, because (80) (0.173) & (80) (1-0.173) are both at least 10. This means we can use the normal distribution to model the distribution of sample proportions.

Coffee: the popular chain of cafés have been receiving online complaints about one store location. Regular customers complain that the staff at this location consistently under fill their cups of coffee. The owner of that train. I'll personally visit the location to meet with the staff to determine if more than 10% of the 15 ounce cups underfilled by one fluid ounce. She arranges to have "mystery shoppers" visit the store. Mystery shoppers are people who are paid to pose as a regular customer and provide feedback to the owner about customer service. After 100 mystery shop visits, she finds that 18 of the 16 ounce cups of coffee underfilled. She plans to test the hypothesis H_0: P equals 0.10 versus H_a: P.> 0.10.

Z = 2.67.

In a fictional study, suppose that the psychologist is studying the effects of daily medication and resting heart rate. Decide call adjust, believe the patients who do not Medicare, I have a higher resting heart rate. For a random sample of 45 pairs of identical, twins, the psychologist randomly assigns one's been to one of two treatments. One twin and each pair medicate daily for one week, all the other 20 is not Medicare. At the end of the week, the psychologist measures the resting heart rate of each month. Assume the main resting heart rate is 80 bpm The psychologist contacts a T test for the mean of the differences in resting heart rate of patients who do not medicate minus resting heart rate of patience to do medicate. Which of the following is the correct no and alternative hypothesis for the psychologist study?

h_0: (Mu) = 0; H_A: (Mu) > 0