📊 statistics

1. The problem involves understanding the formula for the variance of the sampling distribution of the sample proportion $\hat{p}$. 2. The formula given is $$\text{Var}(\hat{p}) =

1. **State the problem:** We want to find a 90% confidence interval for the percentage of all college seniors who would have chosen to attend a different college based on a sample

1. **State the problem:** We need to estimate the mean amount of money spent by 40 shoppers given grouped frequency data. 2. **Formula for mean from grouped data:**

1. **State the problem:** Find the mode of the data set: 11, 12, 12, 9, 9, 11, 9, 15, 15, 10, 11, 12, 11, 12, 12, 13, 11, 12, 13, 12, 12, 11, 9. 2. **Recall the definition of mode:

1. **State the problem:** Find the mode of the data set: 25, 22, 24, 24, 24, 21, 28, 21, 25, 24, 21, 22, 21, 25, 22, 24, 25, 25, 21, 25, 25. 2. **Recall the definition:** The mode

1. **State the problem:** Tina has the data set $\{x, 3, 3, 4, 6\}$. We know the median of this data is 4. We need to find which value of $x$ (either 3 or 6) makes the median 4.

1. The problem asks for the median temperature of 7 consecutive days with temperatures: 20°C, 22°C, 20°C, 24°C, 21°C, 26°C, and 23°C. 2. The median is the middle value in an ordere

1. **State the problem:** We have a sample of ages: $\{17, 29, 22, 54, 31, 16, 63, 48, 29, 36\}$. We need to find the sample mean and the mean absolute deviation (MAD) to evaluate

1. **Stating the problem:** We are given a histogram showing frequency density of sharks at different depth intervals. We want to find the frequency (number of sharks) between dept

1. **State the problem:** We need to estimate the number of gold rings with mass between 1.4 g and 3 g using the histogram data. 2. **Recall the formula for frequency from a histog

1. The problem is to find the regression line for the scatter plot of crime rate vs. poverty rate. 2. The regression line is given by the formula $$y = mx + b$$ where $m$ is the sl

1. **State the problem:** We have a survey of 400 students about where they keep their phones while sleeping. We need to find: (a) The percentage of students who keep their phone i

1. **State the problem:** We are given a sample of net worth values (in millions) and asked to find the confidence interval estimate for the population mean $\mu$. 2. **Data given:

1. **State the problem:** Dana wants to test if the wave heights follow a normal distribution using a chi-square goodness-of-fit test at the 5% significance level. 2. **Formula for

1. **Problem:** Decide whether each distribution (a to f) is approximately bell-shaped based on the histogram descriptions. 2. **Recall:** A bell-shaped distribution is symmetric,

1. **Problem statement:** Explain how the histograms of simulated samples demonstrate the Central Limit Theorem (CLT) for sample means and comment on the "rule of thumb" about samp

1. The problem asks for the probability of exactly 1 success in a binomial distribution with $n=6$ trials and probability of success $p=0.80$. 2. The binomial probability formula i

1. **State the problem:** We are given a mean platelet count of $255.1$ and a standard deviation of $65.2$. We want to use Chebyshev's theorem to find the minimum percentage of wom

1. The problem asks us to interpret a box plot representing classroom attendance last month. 2. A box plot shows the distribution of data using five key points: minimum, first quar

1. The problem is to construct a stem-and-leaf plot from the given data sets. 2. A stem-and-leaf plot organizes data by place value: the "stem" represents the leading digit(s), and

1. The problem involves interpreting a frequency distribution table for fish lengths. 2. The table shows intervals of fish lengths $l$ in centimetres and the number of fish in each