Building Blocks
A researcher records the zip code of every person who enters a local shopping mall. What type of data is being collected – qualitative, or quantitative?
Identify which type of graph would be most appropriate for the following scenario: A local bookstore wants to track the total number of books sold each day over the month of October to identify sales trends.
A. Pie Chart
B. Time Series Graph
C. Scatter-plot
D. Stem-and-leaf Plot
B. Time Series Graph
A standard six-sided die is rolled once. What is the probability of rolling a number greater than 2?
3/6 or 1/2
Which of the following is a characteristic of the Standard Normal Distribution?
A. The mean is 1 and the standard deviation is 0.
B. The total area under the curve is exactly 1.
C. The curve touches the x-axis at exactly three standard deviations.
D. The distribution is skewed to the right.
B. The total area under the curve is exactly 1.
Consider the confidence interval (45.8, 72.6). Calculate the sample mean and margin of error that were used to create the interval.
Sample Mean: 59.2
Margin of Error: 13.4
A news organization polls every 50th person listed in a city's phone directory to ask about their voting preferences. Which sampling technique is being used – systematic, stratified, simple random, or cluster?
Systematic sample
Find the Mean, Median, and Mode for the following data set: 4, 7, 2, 8, 4, 5, 10
Mean: 5.71
Median: 5
Mode: 4
In a sample of 162 juniors and seniors, 97 juniors and 46 seniors took the SAT this year, while 10 juniors and 9 seniors took the ACT. Find the probability that a randomly chosen student from this sample is a senior or took the ACT.
65/162
The length of a specific species of fish is normally distributed with a mean of 15 inches and a standard deviation of 2 inches. What is the probability that a randomly selected fish is shorter than 18 inches?
0.9332
Find the critical z-value for an 82% confidence interval.
1.341
In a study of 4,000 adults in a certain state, it was found that 25% have at least one pet. Is the value '25%' an example of a: census, variable of interest, statistic, or parameter?
Statistic
If a data set for house prices in a specific neighborhood is skewed right, which of the following statements must be true?
A. The Mean is equal to the Median.
B. The Mean is less than the Median.
C. The Mean is greater than the Median.
C. The Mean is greater than the Median.
A local club has 20 members. If the club needs to elect a President, Vice President, and Secretary, how many different ways can these three offices be filled?
6840
On a professional certification exam, scores are normally distributed with a mean of 300 and a standard deviation of 40. If a "passing score" is defined as the 80th percentile, what is the minimum score required to pass? Round to the nearest whole number.
334
You have just taken a random sample of size n = 20. The population is normal, and the population standard deviation is not known. Should you use the standard normal distribution, the t-distribution, or neither when creating a confidence interval using this sample?
t-distribution
A medical study investigates a new headache medication. Group A receives the pill, while Group B receives a sugar pill that looks identical. Neither the patients nor the doctors administering the pills know which group is which. What type of experimental design was used?
Double-blind Experiment
The weights of newborn babies at a hospital are normally distributed with a mean of 7.5 lbs and a standard deviation of 0.5 lbs. According to the Empirical Rule, what percentage of babies weigh between 6.5 lbs and 8.5 lbs?
95%
A bag contains 15 marbles: 6 yellow, 3 blue, 2 green, and 4 red. You pick one marble, and without replacing it, you pick a second. What is the probability that the first marble is green and the second is yellow?
12/210 or 2/35
According to the Central Limit Theorem, a sampling distribution of sample means can be considered normal if it meets one of two conditions. One condition is if the population is already normally distributed. What is the other condition?
n > 30
In a survey of 500 first graders, 100 students stated that yellow was their favorite primary color. Construct a 95% confidence interval for the true proportion of first graders who prefer yellow. Round to 3 decimal places.
(0.165, 0.235)
An agricultural researcher wants to test a new fertilizer. They have 40 plots of land: 20 are in a valley with rich soil, and 20 are on a hillside with rocky soil. Why should the researcher use a 'Randomized Block Design' instead of a 'Completely Randomized Design'?
To control for the confounding variable
You are analyzing the test scores of a small class: 72, 78, 80, 82, 88. A student from another class scored a 98. Is their score unusual? Explain.
Yes, the score is unusual since it’s more than 2 standard deviations above the mean.
How many distinguishable ways can you rearrange the letters in the word "STATISTICS"?
50,400
A manufacturer claims that their lightbulbs have a mean life of 1,200 hours with a standard deviation of 100 hours. Assume the life of these bulbs is normally distributed. What is the probability that a random sample of 25 bulbs has an average life greater than 1,230 hours?
0.0668
You want to estimate the mean repair cost of a specific washing machine. If the sample standard deviation is $16, what minimum sample size is needed to be 90% confident that the sample mean is within $3.50 of the population mean?
57