Inferences from Data
Which assumption will work best for a large data set with a normal distribution?
Most of the data points are close to the mean value of the set.
Type the correct answer in the box. Use numerals instead of words. An experiment is set up to study the weights of 45 frogs after they are given a hormone treatment. The population mean is 22.70 grams with a standard deviation of 2.96 grams. What is the standard error of the sample mean? Round your answer to the nearest hundredth. The standard error of the sample mean is approximately
NOT NOT NOT .441
The mean of the scores obtained by a class of students on a physics test is 42. The standard deviation is 8. Students have to score at least 50 to pass the test. Assuming that the data is normally distributed, approximately _____% of the students passed the test.
NOT NOT NOT 84
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). A test to detect an infection gives a positive result 98% of the time when an infection is present. It is 97% accurate when an infection is not present. % of results will be false negatives, and % of results will be false positives.
NOT THESE: 3, 2
A food store owner wants to determine the type of products customers prefer to buy. The owner surveyed 40 customers on a day when the store had 335 customers, and found that 40% of those surveyed preferred to buy organic products over non-organic products. Assuming a 95% confidence level, which statement holds true?
NOT THIS ONE: As the sample size is too small, the margin of error cannot be trusted.
Based on probability and if it is appropriate for a decision to be left up to chance, choose every situation that is both statistically fair and morally fair.
Situations 3 and 5: 5 cousins and 5 roomates
Suppose an opinion poll predicted that, if the election were held today, the major party would win 68% of the vote. If the pollster attached a 95% confidence level to the interval 68% plus or minus 4%, what would that mean?
That there is a 95% chance that the major party will win between 64% and 72% of the vote.
Gavin collects a certain type of seashell. He has 160 seashells. The seashells' weights are distributed normally, with a mean of 120 grams and a standard deviation of 26 grams. How many of the seashells weigh at least 68 grams?
156
Raw scores on a certain standardized test one year were normally distributed, with a mean of 156 and a standard deviation of 23. If 48,592 students took the test, about how many of the students scored less than 96?
220
A survey of the students in Lance's school found that 58% of the respondents want the school year lengthened, while 42% think it should remain the same. The margin of error of the survey is 10%. According to the survey data, at least _____% of students want the duration of the school year to remain the same, and at least _____% want the school year to be lengthened.
32, 48
The scores of eighth-grade students in a math test are normally distributed with a mean of 57.5 and a standard deviation of 6.5. From this data, we can conclude that 68% of the students received scores between ____ and ____.
51, 64
A set of data has a sample mean of 65.4 and a standard deviation of 1.2. If the sample size is 45, what is the 99% confidence interval of this data?
64.94 and 65.86
The speed of nitrogen molecules in the atmosphere (at 20ºC) follows a normal distribution with a mean speed of 500 meters/second and a standard deviation of 50 meters/second. Which conclusion does this information best support?
68% of the molecules have speeds between 450 meters/second and 550 meters/second.
Jorge conducted a survey by asking 120 students whether they use a pencil to take notes. Of the students surveyed, 90 responded favorably. Which margin of error matches each confidence level for this situation?
90% = .065, 95% = .077, 99% = .102
Two manufacturers of sport utility vehicles claim that the sharpness of the turning radius for their SUV is better than all other SUVs on the market. John randomly selected 30 professional sports car drivers to test the manufacturers' claims. The drivers were all experienced in driving both manufacturers' SUVs as well as competing SUVs on the market. He asked 15 drivers their opinion of vehicle A and 15 drivers their opinion of vehicle B. The drivers' opinions on both SUV manufacturers' claims are shown in the table.
NOT THIS ONE: Only the claim for vehicle B is true because more people agree with their claim.
The programmer at a local public radio station is compiling data on listeners who stream podcasts. An executive for the national broadcaster has communicated that the overall population mean is 20,500 with a standard deviation of 2,180. The local programmer has a sample of 30 podcasts for her station. By the central limit theorem, which interval do about 99.7% of the sample means fall within?
NOT THIS ONE: 20,102 and 20,898
The coach of a college baseball team is comparing the wins of two rival teams in the division. The number of wins per season for each team is shown in the chart. Based on the chart, the coach determined that in 2016, the Tigers won roughly half the number of games as the Stars. Is this analysis correct?
No, because the vertical scale begins at 20, and the distance between the lines doesn't reflect the actual values.
An electronics store advertises that one lucky customer will be given a television at the store's 10th anniversary celebration. On the day of the celebration, 150 customers, of which 82 are less than 30 years old and 68 are 30 years old or more, complete a form to enter for the chance to win the television. The manager of the store wants to select the winner by drawing a form out of a box, but the box can only hold 100 forms. Which method ensures both that the manager can use the box for the selection and that each customer has a fair chance of winning?
Randomly divide the 150 forms into three equal-sized lots. Then, randomly select two of the lots and place them in the box. Randomly select the winning customer's form out of the box.
Ron coaches a baseball team. There are three innings left in the game, and the team is losing by four runs. Ron is trying to decide whether to replace the pitcher or keep the pitcher in for another inning. In the past, when losing by four runs, he has replaced the pitcher a total of 14 times and kept the pitcher in a total of 10 times. The table shows the results of those decisions at the end of nine innings. Replaced pitcherKept pitcherWon game84Lost game45Tied game21Total1410 Based on the information in the table, if the goal is to win the game in nine innings, should Ron replace the pitcher or keep the pitcher in?
Ron should replace the pitcher with a relief pitcher.
Drag the values to the correct locations on the image. Not all values will be used. Jeremy is conducting a survey about his coworkers' in-office water consumption to encourage management to install more water dispensers at their location. He found that the population mean is 112.5 ounces with a standard deviation of 37.5. Jeremy has a sample size of 96. Complete the equation that Jeremy can use to find the interval in which he can be 99.7% sure that the sample mean will lie.
See Image
Melinda conducted an experiment regarding the effectiveness of two graphic design training courses, Image-nation and Perfect Pics. She randomly selected 20 people from her marketing team and assigned 10 team members to each training course. To determine the effectiveness of Image-nation and Perfect Pics, Melinda assigned the same task to all participants at the beginning and at the end of each program. She stated that a training course is effective if there is a decrease in time required to complete a graphics task. At the beginning of each course, Melinda found the average time to complete a task for Image-nation participants to be 60 minutes and the average time to complete a task for Perfect Pics participants to be 70 minutes. At the end of each training course, Melinda found the time taken to complete a task for Image-nation participants to be 50 minutes and the average time to complete a task for Perfect Pic par
The Image-nation course and the Perfect Pics course are both effective because the average time to complete a task decreased for each course; however, Perfect Pics is the more effective course because it yielded a greater decrease in the average time to complete a task.
Fastex Shoes claims that it has designed a new range of lightweight shoes that allow athletes to run faster than they can using any other shoes. SportsPlus, a rival shoe manufacturer, then came up with a design that it claims performs even better than Fastex's design. A sports magazine decided to test the claims. It created two groups of 15 randomly selected athletes each. Members of both groups were pretested and determined to have equal athletic ability. Additionally, they followed the same nutrition plan and training program during the study. The athletes did a 1-mile run to test the shoes. The magazine found that the athletes who used Fastex shoes had reduced their 1-mile run time by an average of 3%, and athletes who used SportsPlus shoes had reduced their 1-mile run time by an average of 2%. Given the magazine's data collection method and findings, what conclusion can be made?
The data collection method used was fair since both shoe designs were tested on identical parameters.
A group of crafters is collecting data on the amount of yarn they use for each scarf knitted. Each person collected 12 pieces of data and will compile that data to determine a population mean. One crafter, Chris, has a sample mean of 200 meters of yarn. Which statement must be true about this situation?
There is not enough information to make a conclusion about the population mean.
Select all the studies in which the results may have been skewed by bias.
see image
Select the correct answer. As the number of samples increases, which value can be used to approximate a population mean?
the mean of the sample means
Which statement best describes a margin of error?
the value of error between a sample statistic and an actual population parameter