stats final

34. In a recent poll of 1200 randomly selected adult office workers, 32% said they had worn a Halloween costume to the office at least once. Report the 95% confidence interval for the proportion of all adult office workers who have worn a Halloween costume to the office at least once. Round final calculations to the nearest tenth of a percent.

(29.4%, 34.6%)

17. Three scatterplots are shown below. The calculated correlations are − 0.88, 0.00, and 0.68. Determine which correlation goes with which scatterplot.

(A) (1) 0.00 (B)(1) 0.68 (C)(3) -0.88

42. Feature movie lengths (in hours) were measured for all movies shown in the past year in the U.S. The mean length of all feature length movies shown was 1.80 hours with a standard deviation of 0.15 hours. Suppose the length of a random sample of 20 movies was recorded from all movies released this year. The mean length of the feature length movies was found to be 1.72 hours with a standard deviation of 0.18 hours. What is the standard error for the estimated mean feature length movie time of the 20 randomly selected movies? Round to the nearest thousandth.

0.034

21. A university conducted a survey of 277 Sophomore, Junior, and Senior undergraduate students regarding satisfaction with student government. Results of the survey are shown in the table by class rank.

0.069

12. Use the following information to answer the question. The mean age of lead actresses from the top ten grossing movies of 2010 was 29.6 years with a standard deviation of 6.35 years. Assume the distribution of the actresses' ages is approximately unimodal and symmetric. Between what two values would you expect to find about 95% of the lead actresses ages?

16.9 and 42.3 years

*25. A random number generator is set to generate single digits between 0 and 9. One hundred fifty random numbers are generated. The probability distribution for this random number generator is given below. What is the mean of this distribution? Round to the nearest tenth. x0123456789 P(x) 0.09 0.12 0.11 0.08 0.09 0.13 0.10 0.07 0.10 0.11

4.5

32. A group of battery powered toys produced in a day at a factory has a defect rate of 0.5%. Suppose a quality inspector randomly inspects 200 of the toys. Complete the following statement: The quality inspector should expect ____defective toys, with an error of ____.

A- 1;0.5%

A dot plot of the speeds of a sample of 50 cars passing a policeman with a radar gun is shown below. What proportion of the motorists were driving above the posted speed limit of 55 miles per hour?

A-0.50

5. Researchers conducted a study and determined that students who participate in sports are happier than students who do not. Can we conclude that participating in sports makes students happier?

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

7.The histogram shows the distribution of pitch speeds for a sample of 75 pitches for a college pitcher during one season. Which of the following statements best describes the distribution of the histogram below?

A-The distribution is symmetric around a pitch speed of about 93 mph.

16. Doctors hypothesize that smoking cigarettes inflames the bronchial tubes and so makes it harder to breathe. They measured the lung capacity (in liters) and the number of cigarettes smoked in a typical day for a sample of adults. Is the scatterplot to the right consistent with the researcher's hypothesis? Yes, it is consistent. No, it contradicts this hypothesis. There is no evidence in support or contradiction of the hypothesis. ID: 4.1-6

A-Yes, it is consistent.

27. The length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with a mean of 3 minutes and a standard deviation of 1 minute. Find the probability that a randomly selected college student will take between 1.5 and 4 minutes to find a parking spot in the library lot. Round to four decimal places.

A. 0.7745

28. The average travel time to work for a person living and working in Kokomo, Indiana is 17 minutes. Suppose the standard deviation of travel time to work is 4.5 minutes and the distribution of travel time is approximately normally distributed. Approximately what percentage of people living and working in Kokomo have a travel time to work that is less than 15.5 minutes? Round to the nearest whole percent.

A. 37%

2. The two-way table below shows the survey results when sixty adults were asked whether they had made a clothing purchase in the last thirty days. Of the adult males surveyed, what percentage had made a clothing purchase in the last thirty days?

A. 50%

14. Use the accompanying information to answer the question. Here is a table recording the number of deaths for the top thirteen worst U.S. tornados since 1925. A histogram showing the distribution is also included. Estimate the most appropriate measure of variability.

B-IQR; 156

33. A pollotarian is a person who eats poultry but no red meat. A wedding planner does some research and finds that approximately 3.5% of the people in the area where a large wedding is to be held are pollotarian. Treat the 300 guests expected at the wedding as a simple random sample from the local population of about 200,000. Suppose the wedding planner assumes that 5% of the guests will be pollotarian so she orders 15 pollotarian meals. What is the approximate probability that more than 5% of the guests are pollotarian and therefore she will not have enough pollotarian meals? Round to four decimal places.

B. 0.079

22. Use the following table to answer the question. A random sample of college students was asked to respond to a survey about how they spend their free time on weekends. One question, summarized in the table below, asked each respondent to choose the one activity that they are most likely to participate in on a Saturday morning. The activity choices were homework, housework, outside employment, recreation, or other.

B. 0.163

20. Use the following table to answer the question. A random sample of college students was asked to respond to a survey about how they spend their free time on weekends. One question, summarized in the table below, asked each respondent to choose the one activity that they are most likely to participate in on a Saturday morning. The activity choices were homework, housework, outside employment, recreation, or other.

B. 0.52

10. Find the standard deviation for the given sample data. Round your answer to one more decimal place than is present in the original data. The top nine scores on the organic chemistry midterm are as follows. 72, 89, 87, 74, 28, 46, 53, 48, 73

B. 20.6

50. The following numbers are the differences in pulse rate (beats per minute) before and after running for 12 randomly selected people. Positive numbers mean the pulse rate went up. Test the hypothesis that the mean difference in pulse rate was more than 0, using a significance level of 0.05. Assume the population distribution is Normal. 23, 13, 10, 10, 14, 9, 0, 2, 10, 41, 0, and 15Determine the null and alternative hypotheses. Choose the correct answer below.

B. H0: =0 Ha: >0 t-stat=3.78 p-value=0.002 less than or equal to reject suffiecent

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

Bar graph and pie chart

9. Two Physics classes at Jefferson High School took the same quiz. Mr. Spears had 20 students in his class with a mean score of 80. Mrs. Guyton's class of 30 students had a mean score of 90. Overall, what was the mean score for all students on the quiz?

C. 86

15. Use the side-by-side boxplots below to answer the question. The boxplots summarize the number of sentenced prisoners by state in the Midwest and West. Based on the boxplot for the West, which of the following is true?

C.25% of the states sentenced more than 15,706 prisoners.

26. Suppose that the probability that a person books a hotel using an online travel website is 0.68. For the question that follows, consider a sample of fifteen randomly selected people who recently booked a hotel. What is the probability that at least fourteen out of fifteen people used an online travel website when they booked their hotel? Round to three decimal places.

D. 0.022

23. Suppose that a recent poll of American households about car ownership found that for households with a car, 39% owned a sedan, 33% owned a van, and 7% owned a sports car. Suppose that three households are selected randomly and with replacement. What is the probability that none of the three randomly selected households own a van? (Round to the nearest thousandth)

D. 0.301

29. The amount of rainfall in January in a certain city is normally distributed with a mean of 3.6 inches and a standard deviation of 0.6 inches. Find the value of the 25th percentile, rounded to the nearest tenth.

D. 3.2

45. The weights at birth of five randomly chosen baby Orca whales were 425, 454, 380, 405, and 426 pounds. Assume the distribution of weights is normally distributed. Find a 95% confidence interval for the mean weight of all baby Orca whales. Use technology for your calculations. Give the confidence interval in the form "estimate ± margin of error". Round to the nearest tenth of a pound.

D. 418.0 ± 34.1 pounds

19. The accompanying scatterplot shows the relationship between the ages of women when they first married and the ages when they had their first child. The correlation coefficient between the values is 0.9315. 4 Click the icon to view the scatterplot. The regression equation for the data isAge − first child = 6.404 + 0.955 • (Age-married) Can we use the regression equation to predict the age at which a woman has her first child for a woman who first married at the age of 50?

D. No, we cannot make a prediction because a woman who marries at age 50 is outside the range of our data. We would be extrapolating.

18. Use the following regression equation regarding professor salaries to answer the question. Salary = 95000 + 1280 • (Years) Note that Years is the number of years a professor has worked at a college, and Salary is the annual salary (in dollars) the professor earns. Interpret the slope in the context of the data.

D. The slope is 1280. For every additional year a professor works at a college, his/her salary is predicted to increase by $1,280.

24. Determine whether the variable would best be modeled as continuous or discrete.The number of cups dispensed from a beverage vending machine during a 24-hour period.

Discrete

49. An economist conducted a hypothesis test to test the claim that the average cost of eating a meal away from home decreased from 2009 to 2010. The average cost of eating a meal away from home in 2009 was $7.15 per person per meal. Assume that all conditions for testing have been met. He used technology to complete the hypothesis test. Following is his null and alternative hypothesis and the output from his graphing calculator. Choose the statement that contains the correct conclusion regarding the hypothesis and the original claim. 5 Click the icon to view the hypotheses and graphing calculator output.

Fail to reject the null hypothesis; there is not sufficient evidence to support the claim that the average cost of eating away from home has decreased since 2009.

37. Read the following problem description then choose the correct null and alternative hypothesis. A new drug is being tested to see whether it can reduce the rate of asthma attacks in children ages 5 to 14. The rate of asthma attacks in the population of concern is 0.0744.

H0: p = 0.0744; Ha: p < 0.0744

a. Do a majority of adults (more than 50%) support a ban on sugary snacks and soft drinks? Perform a hypothesis test using a significance level of 0.05. State the null and alternative hypotheses. Note that p is defined as the population proportion of people who believe that schools should ban sugary foods.

H0:p=0.50 z=2.68 p-value=0.004 reject The percentage of all adults who favor banning is significantly more than 50%.

47. According to the website www.costofwedding.com, the average cost of flowers for a wedding is $698. Recently, in a random sample of 40 weddings in the U. S. it was found that the average cost of the flowers was $734, with a standard deviation of $102. On the basis of this, a 95% confidence interval for the mean cost of flowers for a wedding is $701 to $767. Choose the statement that is the best interpretation of the confidence interval.I. That probability that the flowers at a wedding will cost more than $698 is greater than 5%.II. In about 95% of all samples of size 40, the resulting confidence interval will contain the mean cost of flowers at weddings.III. We are extremely confident that the mean cost of flowers at a wedding is between $701 and $767.

II and III are both correct.

35. A random sample of 830 adult television viewers showed that 52% planned to watch sporting event X. The margin of error is 3 percentage points with a 95% confidence. Does the confidence interval support the claim that the majority of adult television viewers plan to watch sporting event X? Why?

No; the confidence interval means that we are 95% confident that the population proportion of adult television viewers who plan to watch sporting event X is between 49% and 55%. The true proportion could be less than 50%.

1. The number of parents who attended parent teacher conferences at a local elementary school is an example of what type of variable?

Numerical variable

44. What can a confidence level of a confidence interval be thought of as?

The "job performance" of the confidence interval

13. Exam 1 scores have a mean of 500 and a standard deviation of 90, while exam 2 scores have a mean of 20 and a standard deviation of 3. Assuming both types of scores have distributions that are unimodal and symmetric, which is more unusual: an exam 1 score of 750 or an exam 2 score of 28?

The exam 1 score is more unusual.

36. In hypothesis testing, the null hypothesis is best described by which of the following statements?

The null hypothesis always gets the benefit of the doubt and is assumed to be true throughout the hypothesis testing procedure.

38. A janitor at a large office building believes that his supply of light bulbs has too many defective bulbs. The janitor's null hypothesis is that the supply of light bulbs has a defect rate of p = 0.07 (the light bulb manufacturer's stated defect rate). Suppose he does a hypothesis test with a significance level of 0.05. He randomly selects 300 light bulbs and finds 27 that are defective. Symbolically, the null and alternative hypothesis are as follows H0: p=0.07 and Ha: p>0.07. The janitor calculates a p-value for the hypothesis test of approximately 0.087. Choose the correct interpretation for the p-value.

The p-value tells us that if the defect rate is 0.07, then the probability that the janitor will have 27 or more defective light bulbs out of 300 is approximately 0.087. At a significance level of 0.05, this would not be an unusual outcome.

39. A researcher conducts a hypothesis test on a population proportion. Her null and alternative hypothesis areH0: p=0.6 and Ha: p < 0.6 . The test statistic and p-value for the test are z= −1.51 and p value=0.0655. For a significance level of = 0.05, choose the correct conclusion regarding the null hypothesis.

There is insufficient evidence to reject the null hypothesis that the population proportion is equal to 0.6.

31. A researcher is interested in knowing how many students of a particular college would be interested in having a sandwich shop open within a block of campus. She surveys 300 students on campus at different times of day by asking students randomly if they would answer a few questions. She receives a response from 35. Of those who responded, 65% favored having a sandwich shop within a block of campus. This scenario describes sampling bias. Which statement most accurately describes the bias? I. The researcher asked only one question which results in bias. II. The students voluntarily responded which could result in bias. III. Not enough students responded which can result in bias.

both II and III

An education researcher randomly selects 25 of the nation's junior colleges and interviews all of the professors at each school.

cluster

4. Indicate whether the study described is an observational study or a controlled experiment.A group of cancer patients is divided into two groups. One group is given a new drug to fight the side effects of chemotherapy and the other group is given a placebo. After three months, they are asked to respond to a questionnaire about the frequency and severity of their side effects to see whether the new drug improved the overall negative side effects of chemotherapy.

controlled experiment

A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants in the 40-44 age group was taken and the mean finishing time was found to be 1.62 hours with a standard deviation of 0.40 hours. Suppose we were to make a histogram of the finishing times of the 30 participants in the 40-44 age group. Would the histogram be a display of the population distribution, the distribution of a sample, or the sampling distribution of means?

distribution of a sample

11. For the pair of accompanying histograms, determine which distribution has the larger standard deviation.

has a larger standard deviation than (ii).

46. Many couples believe that it is getting too expensive to host an "average" wedding in the United States. According to the website www.costofwedding.com, the average cost of a wedding in the U.S. in 2009 was $24,066. Recently, in a random sample of 40 weddings in the U.S. it was found that the average cost of a wedding was $23,224, with a standard deviation of $2,903. On the basis of this, a 95% confidence interval for the mean cost of weddings in the U.S. is $22,296 to $24,152. Does the confidence interval provide evidence that the mean cost of a wedding has decreased?

no

A useful estimator for the population mean is the _______. A useful estimator for the population mean is the (1)

sample mean

30. A magazine publisher mails a survey to every subscriber asking about the timeliness of its subscription service. The publisher finds that only 6% of the subscribers responded. This 6% represents what?

the sample