Intro Stats

A sample of 650 millenials showed that 32% of them lease their first car. Find the 95% confidence interval for the proportion of all millennials who lease their first car. Round your answer to 3 decimal places.

(0.284, 0.356)

Test results from the second statistics exam were normally distributed with a mean score of 76 and a standard deviation of 6.8. Kendra's score was in the 85th percentile (in other words, she scored as high or higher than 85% of students). What was Kendra's score on the test? (Use either your graphing calculator or a standard normal table.)

83

A pescatarian is a person who does not eat meat, but does eat fish A wedding planner does some research and finds that approximately 3.5% of the people in the area are pescatarian. The wedding planner expects 300 guests. What is the approximate probability that more than 5% of the guests are pescatarian? Assume all conditions of the Central Limit Theorem are satisfied. Round to the nearest thousandth.

0.079

Suppose that the average length of a YouTube video posted on the the internet is 4.3 minutes with a standard deviation of .75 minute. It is known that YouTube video length is not normally distributed. Suppose a sample of 25 YouTube videos is taken from the internet. What is the approximate probability that the sample average YouTube video length will be more than 4.5 minutes? Hint: You will need to use your z-chart to answer this.

0.091

The mean annual salary at a small manufacturing company is $47,312 with a standard deviation of $6,375. What is the probability that a randomly chosen employee is making over $55,000 a year? Assume salaries are normally distributed. Round to 3 decimal places

0.114

In a certain class of students, there are 8 boys from Wilmette and 10 girls from Wilmette, 3 boys from Kenilworth and 5 girls from Kenilworth, 4 boys from Glencoe and and 8 girls from Glencoe. If the teacher calls upon a student to answer a question, what is the probability that the student will be from Kenilworth?

0.211

In one large city, 73% of adults have health insurance. What is the probability that 2 adults selected at random from this city both have health insurance? Round to the nearest thousandth if necessary

0.533

Find the z-score for which the area under the standard normal curve to its left is 0.72

0.58

Suppose the average travel time to work for a person living and working in Louisville, KY is 26.0 minutes with a standard deviation of 1.5 minute. Assume that the travel times of workers in Louisville are approximately normally distributed. If a worker in Louisville is randomly selected, what is the probability that his/her travel time will be between 23 and 26.5 minutes? Round to 3 decimal places

0.608

A random sample of 17 independent female college-aged dancers showed a sample mean height of 62.6 inches and a sample standard deviation of 2.1 inches. Assume that this distribution of heights is Normal. A researcher wishes to find a 90% confidence interval. What value should he use for the t-multiplier? Hint: Use the t-critical values chart.

1.746

Suppose a new app is being tested to see whether it can increase the rate of college students who exercise intensely three or more times a week for at least 20 minutes . Suppose also that the current rate in the population of concern is 0.436. Would the hypothesis test needed be a left-tailed test, a right-tailed test, or a two-tailed test?

right-tailed

Identify the type of sampling used. A researcher randomly selected one adult from the first 10 that walked into an airport, then selected every 10th adult from that one for extra security screening. What sampling technique is she using?

systematic

Suppose a consumer product researcher wanted to find out whether a printer ink cartridge lasted longer than the manufacturer's claim that their ink cartridges could print 400 pages. The researcher tested 40 ink cartridges and recorded the number of pages that were printed before the ink started to fade. Test the hypothesis that the ink cartridges lasted for more than 400 pages. Following are the summary statistics: = 415 pages, s = 30 pages Report the t-statistic.

t = 3.162

A store manager kept track of the number of newspapers sold each week over a seven-week period. The results are shown below. The Interquartile Range (IQR) is 187. Interpret the IQR in the context of the problem. 53, 11, 219, 111, 300, 240, 233

the middle 50% of the number newspapers sold has a range of 187.

Which one of the random variables listed below is continuous?

the time spent in line for a new rollercoaster at Cedar Point

In 2007, the mean price per pound of lobster in New England was $11.48 and the standard deviation was $2.12. A histogram of the data shows that the distribution is unimodal and symmetric. A local New England grocer is selling lobster for $8.99 per pound. What is this price in standard units? Assuming the Empirical Rule applies, would this price be considered unusual or not? Round to the nearest hundredth.

z = -1.17; This price would not be unusual.

A researcher carried out a hypothesis test using a two-tailed alternative hypothesis. Which of the following z-scores is associated with the smallest p-value?

z = 2.68

A large state university conducted a survey among their students and received 400 responses. The survey asked the students to provide the following​ information: ​*Age ​*Year in School​ (Freshman, Sophomore,​ Junior, Senior) ​*Major What type of graph would you use to describe the variable​ Age?

A histogram because Age is a numerical variable.

The null hypothesis is always a statement about which of the following?

A population parameter

Are the following two events likely to be independent and/or mutually exclusive? Event A: The randomly selected carton of milk you purchased from the store is sour. Event B: Your car​ won't start on a randomly selected morning.

Independent only

Which of the following statements is true about the confidence interval for a population proportion?

It is equal to the sample proportion plus or minus a calculated amount called the margin of error.

When events A and B are said to be independent, what does that mean?

Knowledge that event A occurred does not change the probability that event B occurs.

Complete this statement: As the sample size increases, the standard error of the sample means

decreases.

Which of the following statements is true about experimental and theoretical probability?

If you repeat a random experiment many, many times, your outcomes should on average approach the theoretical probability.

Roll a fair six-sided die. You win $10 if you roll a number less than 4. You will lose $15 if you roll the number 5. If you roll any other number, you will neither win nor lose anything. Find the expected value (winnings) of this probability experiment to the nearest cent.

$2.50

In a recent poll of 1400 randomly selected incoming college students, 343 said that they thought they would withdraw from at least one class in their first academic year. What is the margin of error, using a 95% confidence level, for estimating the true population proportion of incoming college students who thought they would withdraw from at least one class in their first academic year? (Round to the nearest thousandth).

0.023

A national caterer determined that 37% of the people who sampled their food said that it was delicious. A random sample of 144 people is obtained from a population of 5000. The 144 people are asked to sample the caterer's food. If is the sample proportion saying that the food is delicious, what is the standard deviation of the sampling distribution of ?

0.04

Use the following information to answer question #23. The mean age of lead actors from the top ten grossing movies of 2007 was 36.4 years with a standard deviation of 9.87 years. Assume the distribution of the actors ages is approximately unimodal and symmetric. Between what two values would you expect to find about 68% of the lead actors ages?

26.53 and 46.27 years

You are dealt one card from a 52-card deck of playing cards. Find the probability that you are NOT dealt a heart. Express the probability as a simplified fraction. Note: A deck has 4 suits of cards: spades, clubs, hearts, diamonds. There are 13 cards in each suit.

3/4

According to a snack cracker manufacturer, a batch of butter crackers has a defect rate of 6%. Suppose a quality inspector randomly inspects 500 crackers. Complete the following statement: The quality inspector should expect defective crackers, give or take crackers.

30; 5

In a recent school poll, the administrators asked if students were satisfied with the school's course offerings. What is the population of interest here?

All students who attend the school.

Which of the following statements is not true about the normal distribution curve?

Approximately 99.7% of the area lies within 2 standard deviations of the mean.

What are two commonly used graphs to display the distribution of a sample of categorical data?

Bar charts and pie charts

Which of the following is NOT an example of a binomial experiment?

Choosing 20 students in a specific class and listing their eye color

A group of 500 patients who suffer from skin cancer were asked to participate in a study to determine the effectiveness of a new medication. The patients were randomly divided into two groups, one that was given the actual medication and one that received a placebo pill. A good outcome was defined as the cancer being in remission after 6 months of treatment. Is this an example of a controlled experiment or an observational study?

Controlled experiment

When constructing a confidence interval, a larger sample size will _________ the margin of error and the confidence interval will be _________.

Decrease, narrower

Is the following an example of theoretical probability or empirical probability? Kathleen and Kevin roll two dice 50 times and record their results in a chart. They calculate the number of times 7 was rolled. This is an example of what type of probability?

Empirical

Which of the following statements concerning the linear correlation coefficient are true?

If the slope of the regression line is negative, then the linear correlation coefficient is negative. The value of the linear correlation coefficient is always a number between -1 and 1.

Coconut oil has become quite popular in recent years. People who use coconut oil claim it helps with hair care, skin care, stress relief, weight loss, and a boosted immune system. Can we conclude that the use of coconut oil causes these health benefits?

No, the claims are anecdotes and do not give us a true comparison group to find health differences.

Suppose a hypothesis test is conducted where the level of significance and the test statistic results in a p-value = 0.15 . Should the researcher reject the null hypothesis?

No, the researcher should not reject the null hypothesis.

A random sample of likely voters showed that 54% planned to support Measure X. The margin of error is 5 percentage points with a 99% confidence level. Is there evidence to support the claim that Measure X will succeed by receiving a majority of the vote?

No, there is not sufficient evidence to support the claim that the measure will succeed since not all percentages in the interval are above 50%.

Researchers conducted a study and determined that students who carpool have less friends than students who ride the bus to school. Can we conclude that carpooling causes students to have less friends?

No, this is an observational study and we cannot conclude causation.

The bar graph below shows the number of car accidents occurring in one city in each of the years 2001 through 2006. The number of accidents dropped in 2003 after a new speed limit was imposed. A report interprets the graph to mean that the number of accidents dropped by 1/3 after the new speed limit was imposed. Is the report making a correct interpretation?

No. Although the height of the 2003 bar is about 1/3 less than that of the 2002 bar, the bars do not begin at 0 accidents, so the graph does not correctly represent the data. Ninety-eight is not one third less than 120.

A useful estimator for the population mean is the

Sample mean

Researchers are interested in learning more about the age at which registered voters first participated in a federal election. They randomly select 792 registered voters and ask them how old they were when they first voted in a federal election. The mean age of the 792 registered voters when they voted for the first time would be a .

Statistic

The government of a town needs to determine if the city's residents will support the construction of a new town hall. The government decides to conduct a survey of a sample of the city's residents. Which one of the following procedures would be most appropriate for obtaining a sample of the town's residents?

Survey a random sample of persons within each geographic region of the city.

A city planner​ says, "The typical commute to work for someone living in the city limits is less than the commute to work for someone living in the​ suburbs." What does this statement​ mean?

The center of the distribution of commute times for a​ city-dweller is less than the center of the distribution for those living in the suburbs.

Without calculating the standard deviation, compare the standard deviation for the following data sets. (Note: All data sets have a mean of 30.) Which do you expect to have the smallest standard deviation? Explain. Data set 1: 30, 30, 30, 30, 30, 30, 30, 30, 30, 30 Data set 2: 20, 25, 25, 30, 30, 30, 30, 35, 35, 40 Data set 3: 20, 20, 20, 25, 25, 35, 35, 40, 40, 40

The first data set will have the smallest standard deviation since all deviations from the mean are zero and the standard deviation will therefore be zero.

What are the values of the mean and standard deviation for the standard Normal model?

The mean is 0 and the standard deviation is 1.

Suppose we have a data set of the number of car accidents per day in Chicago during the year 2014. The data was input into a spreadsheet manually by an assistant at the Department of Transportation. The lowest number of car accidents of 2014 occurred for one day in July 2014. However, instead of entering 140 car accidents for this one day, the assistant incorrectly entered 14 car accidents. How will this error affect the measures of center for this data?

The mean will be lower than it should be, but the median will not be affected.

The variables height and weight could reasonably be expected to have a positive linear correlation coefficient, since taller people tend to be heavier, on average, than shorter people. Give an example of a pair of variables which you would expect to have a negative linear correlation coefficient.

The miles driven since last fill-up and amount of gas remaining in the tank

With a two-tailed hypothesis test, which one of the following statements is true, given that the test statistic is farther from zero?

The more the null hypothesis is unlikely to be true.

The owner of a 24 hour restaurant wants to determine what items should be removed from the restaurant's menu. She has a market researcher review the receipts of the first 100 customers who come into the restaurant on a Sunday morning to determine what menu items are the most popular. What is wrong with her approach?

The owner took a convenience sample. The 100 customers may not be representative of the population of restaurant customers, so their menu choices may not be representative of all restaurant customers.

A researcher gives a p-value of 0.001 in her analysis. Which definition of p-value is the most accurate?

The probability of observing an outcome as extreme or more extreme than the one observed if the null hypothesis is true.

Suppose Delaware has a total of 105 universities. Of this number, 24 (about 23%) have female presidents. Find a 95% confidence interval for the percentage of Delaware's university presidents who are women or explain why you should not find a confidence interval for the percentage female presidents.

The proportion is the population proportion, not the sample proportion. There is no need for a confidence interval because we already know the population proportion.

In the t-distribution, the degrees of freedom are related to which of the following?

The sample size

Suppose that New Mexico lawmakers survey 160 randomly selected registered voters to see if they favor stricter laws regarding motorcycle helmet use for riders over the age of 17. The lawmakers believe the population proportion in favor of changing the law is​ 5.5% (based on historical data and previous​ votes). Which of the following conditions for the Central Limit theorem are not ​met?

The sample size is too small and will not have enough expected successes.

Suppose we have a distribution of student exam scores on an easy test. What measure of spread would be best to describe this data?

The spread should be described with the IQR because the distribution should be skewed to the left.

A student scores 90 on a geography test and 306 on a mathematics test. The geography test has a mean of 80 and a standard deviation of 20. The mathematics test has a mean of 300 and a standard deviation of 10. If the data for both tests are symmetric and unimodal, on which test did the student score better ?

The student scored better on the mathematics test because the corresponding z-score is farther from 0 than the corresponding z-score on the geography test.

An increasing number of fashion-design houses are offering fitness benefits for their workers. However, one union claims that fewer than 70% of firms in the fashion sector offer fitness benefits. A random sample of 150 fashion-design houses is selected and asked if they offer fitness benefits. The researcher recorded the proportion of these firms that offer fitness benefits and after analyzing the data, she rejected the null hypothesis. Which ONE interpretation below is valid?AA

There's sufficient evidence to support the claim that fewer than 70% of fashion-design houses offer fitness benefits.