# Potential buyers for a new car were randomly divided into two groups. One group was shown the "A" version of an ad for the car, while the other group was shown the "B" version of the ad. All were then tested on their recall of key points made in the ad. The researcher should run a hypothesis test based upon a comparison of means for ? In another study, a healthcare insurance company took measures of subscribers’ cardiac (heart) health. The people were then provided an app for their phones which provided "nudges" and reminders about heart-healthy behaviors, such as eating more vegetables and less fried or fatty food, taking walks and breaks from sitting too long, and getting enough sleep. After 4 months of having the app, the cardiac health measures were taken again, with the objective of

Question
Comparing two groups
Potential buyers for a new car were randomly divided into two groups. One group was shown the "A" version of an ad for the car, while the other group was shown the "B" version of the ad. All were then tested on their recall of key points made in the ad. The researcher should run a hypothesis test based upon a comparison of means for ?
In another study, a healthcare insurance company took measures of subscribers’ cardiac (heart) health. The people were then provided an app for their phones which provided "nudges" and reminders about heart-healthy behaviors, such as eating more vegetables and less fried or fatty food, taking walks and breaks from sitting too long, and getting enough sleep. After 4 months of having the app, the cardiac health measures were taken again, with the objective of seeing if nudges from the app would result in decreased cardiac risk. The researcher should run a hypothesis test based on a comparison of means for?

2021-02-03
Types of independent two sample tests:
Independent two sample test with equal variances.
Independent two sample test with unequal variances.
From the given information, the buyers are divided into two groups. One group shows “A” version of an ad for the car and another group shows “B” version of an ad for the car. That is, the two groups are independent. Hence, both independent samples test with equal variances and independent samples test with unequal variances are used for comparing the means.

### Relevant Questions

The table below shows the number of people for three different race groups who were shot by police that were either armed or unarmed. These values are very close to the exact numbers. They have been changed slightly for each student to get a unique problem.
Suspect was Armed:
Black - 543
White - 1176
Hispanic - 378
Total - 2097
Suspect was unarmed:
Black - 60
White - 67
Hispanic - 38
Total - 165
Total:
Black - 603
White - 1243
Hispanic - 416
Total - 2262
Give your answer as a decimal to at least three decimal places.
a) What percent are Black?
b) What percent are Unarmed?
c) In order for two variables to be Independent of each other, the P $$(A and B) = P(A) \cdot P(B) P(A and B) = P(A) \cdot P(B).$$
This just means that the percentage of times that both things happen equals the individual percentages multiplied together (Only if they are Independent of each other).
Therefore, if a person's race is independent of whether they were killed being unarmed then the percentage of black people that are killed while being unarmed should equal the percentage of blacks times the percentage of Unarmed. Let's check this. Multiply your answer to part a (percentage of blacks) by your answer to part b (percentage of unarmed).
Remember, the previous answer is only correct if the variables are Independent.
d) Now let's get the real percent that are Black and Unarmed by using the table?
If answer c is "significantly different" than answer d, then that means that there could be a different percentage of unarmed people being shot based on race. We will check this out later in the course.
Let's compare the percentage of unarmed shot for each race.
e) What percent are White and Unarmed?
f) What percent are Hispanic and Unarmed?
If you compare answers d, e and f it shows the highest percentage of unarmed people being shot is most likely white.
Why is that?
This is because there are more white people in the United States than any other race and therefore there are likely to be more white people in the table. Since there are more white people in the table, there most likely would be more white and unarmed people shot by police than any other race. This pulls the percentage of white and unarmed up. In addition, there most likely would be more white and armed shot by police. All the percentages for white people would be higher, because there are more white people. For example, the table contains very few Hispanic people, and the percentage of people in the table that were Hispanic and unarmed is the lowest percentage.
Think of it this way. If you went to a college that was 90% female and 10% male, then females would most likely have the highest percentage of A grades. They would also most likely have the highest percentage of B, C, D and F grades
The correct way to compare is "conditional probability". Conditional probability is getting the probability of something happening, given we are dealing with just the people in a particular group.
g) What percent of blacks shot and killed by police were unarmed?
h) What percent of whites shot and killed by police were unarmed?
i) What percent of Hispanics shot and killed by police were unarmed?
You can see by the answers to part g and h, that the percentage of blacks that were unarmed and killed by police is approximately twice that of whites that were unarmed and killed by police.
j) Why do you believe this is happening?
Do a search on the internet for reasons why blacks are more likely to be killed by police. Read a few articles on the topic. Write your response using the articles as references. Give the websites used in your response. Your answer should be several sentences long with at least one website listed. This part of this problem will be graded after the due date.
Use either the critical-value approach or the P-value approach to perform the required hypothesis test. For several years, evidence had been mounting that folic acid reduces major birth defects. A. Czeizel and I. Dudas of the National Institute of Hygiene in Budapest directed a study that provided the strongest evidence to date. Their results were published in the paper “Prevention of the First Occurrence of Neural-Tube Defects by Periconceptional Vitamin Supplementation” (New England Journal of Medicine, Vol. 327(26), p. 1832). For the study, the doctors enrolled women prior to conception and divided them randomly into two groups. One group, consisting of 2701 women, took daily multivitamins containing 0.8 mg of folic acid, the other group, consisting of 2052 women, received only trace elements. Major birth defects occurred in 35 cases when the women took folic acid and in 47 cases when the women did not. a. At the 1% significance level, do the data provide sufficient evidence to conclude that women who take folic acid are at lesser risk of having children with major birth defects? b. Is this study a designed experiment or an observational study? Explain your answer. c. In view of your answers to parts (a) and (b), could you reasonably conclude that taking folic acid causes a reduction in major birth defects? Explain your answer.
Give a full and correct answer Why is it important that a sample be random and representative when conducting hypothesis testing? Representative Sample vs. Random Sample: An Overview Economists and researchers seek to reduce sampling bias to near negligible levels when employing statistical analysis. Three basic characteristics in a sample reduce the chances of sampling bias and allow economists to make more confident inferences about a general population from the results obtained from the sample analysis or study: * Such samples must be representative of the chosen population studied. * They must be randomly chosen, meaning that each member of the larger population has an equal chance of being chosen. * They must be large enough so as not to skew the results. The optimal size of the sample group depends on the precise degree of confidence required for making an inference. Representative sampling and random sampling are two techniques used to help ensure data is free of bias. These sampling techniques are not mutually exclusive and, in fact, they are often used in tandem to reduce the degree of sampling error in an analysis and allow for greater confidence in making statistical inferences from the sample in regard to the larger group. Representative Sample A representative sample is a group or set chosen from a larger statistical population or group of factors or instances that adequately replicates the larger group according to whatever characteristic or quality is under study. A representative sample parallels key variables and characteristics of the large society under examination. Some examples include sex, age, education level, socioeconomic status (SES), or marital status. A larger sample size reduced sampling error and increases the likelihood that the sample accurately reflects the target population. Random Sample A random sample is a group or set chosen from a larger population or group of factors of instances in a random manner that allows for each member of the larger group to have an equal chance of being chosen. A random sample is meant to be an unbiased representation of the larger population. It is considered a fair way to select a sample from a larger population since every member of the population has an equal chance of getting selected. Special Considerations: People collecting samples need to ensure that bias is minimized. Representative sampling is one of the key methods of achieving this because such samples replicate as closely as possible elements of the larger population under study. This alone, however, is not enough to make the sampling bias negligible. Combining the random sampling technique with the representative sampling method reduces bias further because no specific member of the representative population has a greater chance of selection into the sample than any other. Summarize this article in 250 words.
A new vaccine was tested to see if it could prevent the ear infections that many infants suffer from. Babies about a year old were randomly divided into two groups. One group received vaccinations, and the other did not. The following year, only 328 of 2460 vaccinated children had ear infections, compared to 508 of 2453 unvaccinated children. Complete parts a) through c) below. a) Are the conditions for inference satisfied? A. Yes. The data were generated by a randomized experiment, less than 10% of the population was sampled, the groups were independent, and there were more than 10 successes and failures in each group. B. No. It was not a random sample. C. No. The groups were not independent. D. No. More than 10% of the population was sampled.
Researchers wanted to compare the effectiveness of a water softener used with a filtering process with a water softener used without filtering. Ninety locations were randomly divided into two groups of equal size. Group A locations used a water softener and the filtering process, while group B used only the water softener. At the end of three months, a water sample was tested at each location for its level of softness. (Water softness was measured on a scale of 1 to 5, with 5 being the softest water.) The results were as follows: Group A (water softener and filtering) $$\displaystyle{x}_{{1}}={2.1}$$
$$\displaystyle{s}_{{1}}={0.7}$$ Group B (water softener only) $$\displaystyle{x}_{{2}}={1.7}$$
$$\displaystyle{s}_{{2}}={0.4}$$ Determine, at the 90% confidence level, whether there is a difference between the two types of treatments.
The student engineer of a campus radio station wishes to verify the effectivencess of the lightning rod on the antenna mast. The unknown resistance $$\displaystyle{R}_{{x}}$$ is between points C and E. Point E is a "true ground", but is inaccessible for direct measurement because the stratum in which it is located is several meters below Earth's surface. Two identical rods are driven into the ground at A and B, introducing an unknown resistance $$\displaystyle{R}_{{y}}$$. The procedure for finding the unknown resistance $$\displaystyle{R}_{{x}}$$ is as follows. Measure resistance $$\displaystyle{R}_{{1}}$$ between points A and B. Then connect A and B with a heavy conducting wire and measure resistance $$\displaystyle{R}_{{2}}$$ between points A and C.Derive a formula for $$\displaystyle{R}_{{x}}$$ in terms of the observable resistances $$\displaystyle{R}_{{1}}$$ and $$\displaystyle{R}_{{2}}$$. A satisfactory ground resistance would be $$\displaystyle{R}_{{x}}{<}{2.0}$$ Ohms. Is the grounding of the station adequate if measurments give $$\displaystyle{R}_{{1}}={13}{O}{h}{m}{s}$$ and R_2=6.0 Ohms?
A 1300-kg car coasts on a horizontal road, with a speed of18m/s. After crossing an unpaved sandy stretch of road 30.0 mlong, its speed decreases to 15m/s. If the sandy portion ofthe road had been only 15.0 m long, would the car's speed havedecreasedby 1.5 m/s, more than 1.5 m/s, or less than 1.5m/s?Explain. Calculate the change in speed in that case.
Identify the appropriate hypothesis test for each of the following research situations using the options: The null hypothesis, The Test Statistics, The Sample Statistic, The Standard Error, and The Alpha Level.
A researcher conducts a cross-sectional developmental study to determine whether there is a significant difference in vocabulary skills between 8-year-old and 10-year-old children. A researcher determines that 8% of the males enrolled in Introductory Psychology have some form of color blindness, compared to only 2% of the females. Is there a significant relationship between color blindness and gender?
A researcher records the daily sugar consumption and the activity level for each of 20 children enrolled in a summer camp program. The researcher would like to determine whether there is a significant relationship between sugar consumption and activity level.
A researcher would like to determine whether a 4-week therapy program produces significant changes in behavior. A group of 25 participants is measured before therapy, at the end of therapy, and again 3 months after therapy.
A researcher would like to determine whether a new program for teaching mathematics is significantly better than the old program. It is suspected that the new program will be very effective for small-group instruction but probably will not work well with large classes. The research study involves comparing four groups of students: a small class taught by the new method, a large class taught by the new method, a small class taught by the old method, and a large class taught by the old method.
The top string of a guitar has a fundamental frequency of 33O Hz when it is allowed to vibrate as a whole, along all its 64.0-cm length from the neck to the bridge. A fret is provided for limiting vibration to just the lower two thirds of the string, If the string is pressed down at this fret and plucked, what is the new fundamental frequency? The guitarist can play a "natural harmonic" by gently touching the string at the location of this fret and plucking the string at about one sixth of the way along its length from the bridge. What frequency will be heard then?
The dominant form of drag experienced by vehicles (bikes, cars,planes, etc.) at operating speeds is called form drag. Itincreases quadratically with velocity (essentially because theamount of air you run into increase with v and so does the amount of force you must exert on each small volume of air). Thus
$$\displaystyle{F}_{{{d}{r}{u}{g}}}={C}_{{d}}{A}{v}^{{2}}$$
where A is the cross-sectional area of the vehicle and $$\displaystyle{C}_{{d}}$$ is called the coefficient of drag.
Part A:
Consider a vehicle moving with constant velocity $$\displaystyle\vec{{{v}}}$$. Find the power dissipated by form drag.
Express your answer in terms of $$\displaystyle{C}_{{d}},{A},$$ and speed v.
Part B:
A certain car has an engine that provides a maximum power $$\displaystyle{P}_{{0}}$$. Suppose that the maximum speed of thee car, $$\displaystyle{v}_{{0}}$$, is limited by a drag force proportional to the square of the speed (as in the previous part). The car engine is now modified, so that the new power $$\displaystyle{P}_{{1}}$$ is 10 percent greater than the original power ($$\displaystyle{P}_{{1}}={110}\%{P}_{{0}}$$).
Assume the following:
The top speed is limited by air drag.
The magnitude of the force of air drag at these speeds is proportional to the square of the speed.
By what percentage, $$\displaystyle{\frac{{{v}_{{1}}-{v}_{{0}}}}{{{v}_{{0}}}}}$$, is the top speed of the car increased?
Express the percent increase in top speed numerically to two significant figures.
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