Stats Midterm

As part of a class project, a college student wanted to estimate the proportion of students at his college that owned a red car. To estimate this proportion he went to a large student parking lot during the middle of a class day. He found that 325 out of 1037 cars (31%) were red. This sample is best described as:

A professor wanted to determine the proportion of students in his class who have cheated on an exam. The professor selects a random sample of 30 students from his class and emails them the question "Have you ever cheated on an exam?". He receives responses from 10 of the 30 students. Which of the following statements are true? Select all that apply.

Each player in the National Basketball Association is given a jersey number between 0 and 100. The following is a histogram of these NBA jersey numbers.

A market research company is interested in whether or not households in Franklin County, Ohio have cable television. Using the county auditor's list of households the researcher randomly selected 100 homes and contacted the residents. Of the 100 homes it was found that 62 had cable television. Which of the following are true? Select all that apply.

For the SAT college entrance exam (prior to March 2005), the combined scores ranged from 400 to 1600.A study recorded the combined scores from 100 students from each of three schools in a western state.The resulting scores were used to produce these boxplots. Which of the following are true?

An instructor in a college class recently gave an exam that was worth a total of 100 points. The instructor inadvertently made the exam harder than he had intended. The scores were very symmetric, but the average score for his students was 61 and the standard deviation of the scores was 3 points. The instructor is considering 2 different strategies for rescaling the exam results: Method 1:Multiply everyone's score by 1.2. Method 2:Add 9 points to everyone's score. Which of the following are true? Select all that apply.

A college professor stops at McDonald's every morning for 10 days to get a number 1 value meal costing $5.39. On the 11th day he orders a number 8 value meal costing $4.38. Which of the following are true? Select all that apply. Select one or more:

After taking an aptitude test, the computer told Bob that he had a z-score of -1.63. If scores on the aptitude test are normally distributed, which of the following statements can Bob conclude from his score? Select all that apply.

The Mental Development Index (MDI) of the Bayley Scales of Infant Development is a standardized measure used in longitudinal follow-up of high-risk infants. The scores on the MDI have approximately a normal distribution with a mean of 100 and standard deviation of 15. What proportion of children have MDI of at least 88?

For a normal distribution, what standard score (Z-score) has 60% of the distribution above it? Find the closest value listed on the table.

Which of the following are NOT likely to be well modeled by a normal distribution because the distribution is NOT likely to be symmetric?

A state administered standardized reading exam is given to eighth grade students. The scores on this exam for all students statewide have a normal distribution with a mean of 509 and a standard deviation of 84. A local Junior High principal has decided to give an award to any student who scores in the top 10% of statewide scores.

A researcher believes that the ankle circumference for adult females in Europe can be considered to have a normal distribution with a mean of 20 cm.If his belief is correct which of the following ranges of ankle sizes will have the largest proportion of members of this population?

In a Midwestern state an automobile insurance company has a large number of customers. From company files it is known that 77% of the customers have only the state minimums for insurance. An official with the state board of insurance is going to take a random sample of 100 accounts to review. Find the standard deviation of the sample proportion in this situation.

The registrar of a large university knows that 30% of the students come to college with credit for an advance placement (AP) course. The registrar is going to conduct interviews with students regarding their experiences at the university. Depending on which students are chosen, the proportion of students in the sample that have AP credit may vary. In a sample of 100 students, what is the probability that over 36% of the sample has AP credit?

The registrar of a large university knows that 30% of the students come to college with credit for an advance placement (AP) course. The registrar is going to conduct interviews with students regarding their experiences at the university. Depending on which students are chosen, the proportion of students in the sample that have AP credit may vary. In a sample of 200 students, what is the probability that over 31% of the sample has AP credit?

According to a recent report, it was found that 50.3% of residents in Cuyahoga county Ohio are registered to vote. Which of the following is more likely?

At a large university it is known that 40% of the students live on campus. The director of student life is going to take a random sample of 200 students. Which of the following is most likely to occur:

At North Carolina State University it is known that 56% of undergraduates are male. If a sample of 160 undergraduate students was taken, which of the following would accurately describe the sampling distribution? Select all that apply.

Which of the following scenarios involving proportions would be appropriate for conducting inference?

In engineering and product design, it is important to consider the weights of people so that airplanes or elevators aren't overloaded. Based on data from the National Health Survey, we can assume the weight of adult males in the US has a mean weight of 177 pounds and standard deviation of 32 pounds. We randomly select 50 adult males. What is the probability that the average weight of these 50 adult males is over 175 pounds?

The Mental Development Index (MDI) of the Bayley Scales of Infant Development is a standardized measure used in longitudinal follow-up of high-risk infants. The scores on the MDI have approximately a normal distribution with a mean of 100 and standard deviation of 16. We are going to randomly select 64 children and average their MDI scores. What is the probability that the average is under 101?

A large multinational company knows that the average age of their employees is 34 years. They also know that the standard deviation of the ages of these employees is 8 years. We know that the population of employee ages will have a right skewed distribution. A manager from human resources is going to randomly select a sample of 100. Which of the following is true? Select all that apply.

From census data it is known that the average income of households in Wake County is $58,500. It is also known that the distribution of household income in Wake County is strongly skewed to the right with a standard deviation of $14,000. A researcher is going to randomly select a sample of 5 households from Wake County. Which of the following is true? Select all that apply.

At a large university it is known that 40% of the students live on campus. The director of student life is going to take a random sample of 200 students. What is the probability that more than half of the sampled students live on campus?

Consider a normal distribution that has a mean of 0.2 and a standard deviation of 0.04. What value has 1% of this distribution below it? What value has 99% of this distribution below it?

A political action committee wanted to estimate the proportion of county residents who support a change to the county leash law. They took a random sample of 600county residents and found that the proportion who wanted to change the law was 33% with a margin of error of +/- 4% (with 95% confidence). This implies:

The director of human resources at a large corporation takes a random sample of 97 employees. From his sample, he finds that the proportion of their employees that have children is 0.85. What is the standard error of the proportion in this situation?

A sample of 900 college freshmen were randomly selected for a national survey. Among the survey participants, 372 students were pursuing liberal arts degrees. The sample proportion is 0.413. What is the margin of error for a 98% confidence interval for this sample? What is the lower endpoint for the 98% confidence interval?

In a certain city, there are 1 million homes. As part of an environmental status survey, it was desired to estimate the proportion of homes in this city which contain lead based paints. A simple random sample of 150 households revealed that 49 homes had lead based paints in at least one room. What is the sample proportion?

In which of the following scenarios would it be appropriate to construct a 95% confidence interval for the parameter of interest?

The t-distribution has more values at the extremes than a standard normal distribution.

The t-distribution is symmetric.

The t-distribution is centered at its degrees of freedom.

The t-distribution is centered at 0.

The t-distribution has fewer values at the extremes than a standard normal distribution

The t-distribution has a skewed distribution

Assume that from the sample of 18 trees the researcher found that the average height was 4.8 meters with a standard deviation of 0.55 meters. Assume that the distribution of the heights of these trees is not strongly skewed and does not have any outliers. For this sample what is the margin of error for her 99% confidence interval?

A survey of undergraduates at NCSU asked a random sample of 80 students about the amount they had spent on textbooks (in dollars) during the current term. The 95% confidence interval created from this data was $350 ± $40. This interval indicates:

The director of student health at a small high school is studying how many calories students at her high school consume in a day. She takes a random sample of 50 students from the high school and records the number of calories they consume in a 24 hour period. From the sample she found the average number of calories consumed was 1864 and that the standard deviation was 380. However before she finds the confidence interval for how many calories students consume in one day she goes to the statistics teacher for advice. What should the statistics teacher's advice be?

A physiologist was studying the growth of children. As part of this research she was interested in estimating the average length (in centimeters) of the legs of children who were 10 years of age. She took a nationally representative random sample of 10 year old children in the U.S. The resulting data was used to produce the following results.

A regional track championship has decided that they will invite the fastest 15% of runners in their region (runners with the shortest time). The mile time of all potential runners in this region are normally distributed with a mean of 9.5 minutes and a standard deviation of 2.2 minutes. What is the cutoff time for a runner to qualify for the regional track championship?

At a large university it is known that 30% of the students eat at dinning halls on campus. The director of student life is going to take a random sample of 300 students. What is the probability that less than a quarter of the sampled students eat at dinning halls on campus?

Based on data from the National Health Survey, assume the weight of adult females in the US has a mean weight of 142 pounds and standard deviation of 35 pounds. We randomly select 40 adult females. What is the probability that the average weight of these 40 adult females is less than 140 pounds?