Exam 6: Putting Statistics to Work

Provide an appropriate response. -A population consists of 100 professional gymnasts and 100 professional basketball players. For this group, the average height is 70 inches. However, most of the gymnasts are between 57 and 61 inches tall while most of the basketball players are between 78 and 82 inches tall. For this group, observations far from the mean are more common than observations close to the mean. Describe what a boxplot for the heights of this group would look like. Discuss, in particular, the lengths of the whiskers relative to the width of the box and explain your reasoning.

The result of a hypothesis is described in terms of the probability of obtaining a particular sample. Use the given contextto formulate the null and alternative hypotheses. Discuss whether the sample provides evidence for rejecting the nullhypothesis. -A public bus company official claims that the mean waiting time for bus number 14 during peak hours is only 10 minutes. Karen finds this hard to believe as she seems to be invariably late for work. For 42 randomly selected days, her mean waiting time for bus 14 during peak hours was 11.3 minutes. Assuming that the population mean waiting time is 10 minutes , the probability of selecting a random sample with a mean waiting time of 11.3 minutes or more is 0.0026.

Identify the distribution as symmetric, left-skewed, or right-skewed. -The amounts of tax paid by U.S. residents

The result of a hypothesis is described in terms of the probability of obtaining a particular sample. Use the given contextto formulate the null and alternative hypotheses. Discuss whether the sample provides evidence for rejecting the nullhypothesis. -The mayor of a city claims that racial profiling is not a problem in his city. A civil rights group disagrees. The proportion of Caucasians who have been stopped while driving, without good reason, at least once in the past year is $0.19 ( 19 \% )$ . In a random sample of 340 African Americans, the proportion who have been stopped is $0.37 ( 37 \% )$ . Assuming that the proportion of all African Americans in the city that have been stopped is $0.19$ , the probability of selecting a sample in which the proportion who have been stopped is $0.37$ or more is less than $0.001$ .

Provide an appropriate response. -Discuss the differences between the distributions represented by the two boxplots below. Explain your reasoning.

State whether you think the difference between what occurred and what you would expect by chance is statisticallysignificant. -You draw a card at random from a deck of cards and replace it. You repeat this 60 times and get a heart 13 times.

Provide an appropriate response. -In the Florida lottery, the numbers (between 1 and 49)are generated randomly with the expectation that each number has an equal chance of winning. Draw a boxplot which should illustrate the data set of all numbers picked for the lottery during the past year.

Provide an appropriate response. -Weights of adults in a certain age group are normally distributed. Which of the following are plausible values for the mean and standard deviation?

Find the margin of error for the survey results described. -In a poll of 433 adults, 46% said that they favored the proposed environmental laws. Give your answer as a decimal to three decimal places.

State which type of average, the mean, median, or mode, would be most appropriate in the situation described. Explainyour thinking. -A parcel service wants to estimate how many vans it will need. It knows how many parcels are delivered each day, but it also needs to know the average volume of the parcels. Which average would be the most useful?

Use the 68-95-99.7 rule to solve the problem. -For adults in the town of Bridgeport, systolic blood pressure is normally distributed with a mean of 130 mmHg and a standard deviation of 11 mmHg. What percentage of adults in the town have a Systolic blood pressure less than 97 mmHg?

Find a 95% confidence interval for the true population proportion. -In a survey of 257 female employees of a large company, 21% said that they had experienced some form of sexual harassment while working for the company.

Find a 95% confidence interval for the true population proportion. -In a survey of 765 employees of a large company, 32% said that they had high job satisfaction.

Use the range rule of thumb to approximate the standard deviation. -The following is a set of data showing the water temperature in a heated tub at different time intervals. Round results to the nearest tenth. 114.6 115.8 116.7 113.5 113.4 114.6 112.9 115.2

Identify the distribution as symmetric, left-skewed, or right-skewed. -Number of days worked last year by adult males in a U.S. city which has a low unemployment rate

State whether the distribution appears to be (roughly)normal. -

Find the mode(s)for the given sample data. -The speeds (in mi/h)of the cars passing a certain checkpoint are measured by radar. The results are shown below. 40.9 40.0 41.3 40.3 40.7 40.7 40.0 41.9 40.2 40.3 40.9 41.9 40.3 42.8 40.0 44.7 44.7 41.3 43.3 40.9

Find the standard deviation for the given data. Round your answer to one more decimal place than the original data. - $7,15,14,10,10,9,19,19,12$

State how many peaks you would expect for the distribution described. -Numbers of people with birthdays in a particular month (January through December)

Find a 95% confidence interval for the true population proportion. -In a poll of 1082 college students, 19% said that they had cheated at least once on an exam.