📊 statistics

1. **State the problem:** We need to compute the chi-square value using the data from Table 1 and compare it to the rejection region >7.815 at significance level $\alpha=5\%$. This

1. **State the problem:** We have 60 people surveyed, 22 of whom said cycling is their favorite hobby. We want to find the correct angle on a pie chart to mark the cycling section.

1. The problem is to find the central angle of the curry section in a pie chart where the frequency of curry orders is 12 out of a total of 30 meals. 2. The total number of meals o

1. **State the problem:** We want to test if there is a significant difference in the average life of four brands of fluorescent bulbs using one-way ANOVA at the 0.05 significance

1. The problem asks for the probability that in a group of 7 randomly selected U.S. residents, exactly 4 or 5 are in their twenties, given that 19% of U.S. residents are in their t

1. **Problem statement:** We have two brands of smartphones with durability data (in years). We want to find the 90% confidence interval (CI) for the difference in population means

1. The problem asks to determine whether the scenario involves Descriptive or Inferential Statistics. 2. Descriptive Statistics involves summarizing or describing data from a popul

1. **Problem:** Find which batsman, A or B, is more consistent in scoring based on their scores in ten innings. 2. **Step 1:** Calculate the mean (average) score for each batsman.

1. **State the problem:** We want to construct a 99% confidence interval for the difference in proportions of ladies and men who responded in favour of compulsory motor vehicle ins

1. **Problem statement:** Given a random sample $X_1, X_2, \ldots, X_n$ from the probability density function (pdf) $$f(x;\theta) = \theta e^{-\theta x}, \quad x > 0, \theta > 0,$$

1. The problem involves interpreting a cumulative frequency graph showing the mass of dogs and their cumulative frequency. 2. The x-axis represents the mass of dogs in kilograms, r

1. **State the problem:** We need to compute the chi-square value from the data in Table 1 and compare it to the rejection region $x^2 > 7.815$ at $\alpha=5\%$ to decide whether to

1. The problem asks to find the probability that the standard normal variable $Z$ lies between 1.02 and 2.03, i.e., $P(1.02 \leq Z \leq 2.03)$. 2. Recall that for a standard normal

1. **Population**: The entire set of individuals or items of interest in a study. Mathematically, it can be represented as a set $\mathcal{P} = \{x_1, x_2, \ldots, x_N\}$ where $N$

1. The problem asks for the value below which 75% of the widths fall, based on the box plot. 2. In a box plot, the 75th percentile corresponds to the upper edge of the box, also ca

1. The problem asks us to find the range and the interquartile range (IQR) from the given box plot data about centipede leg counts. 2. From the box plot, the minimum value (left wh

1. **Problem statement:** Given a random sample $X_1, X_2, \ldots, X_n$ from the probability density function (pdf) $$f(x;\theta) = \theta e^{-\theta x}, \quad x > 0, \theta > 0,$$

1. **State the problem:** We have two samples representing durability (in years) of two smartphone brands. We want to find the 90% confidence interval (CI) for the difference in po

1. **State the problem:** We want to construct a 99% confidence interval for the difference in proportions of ladies and men who responded in favour of compulsory motor vehicle ins

1. The problem involves interpreting diagnostic plots from a linear regression model where the dependent variable is $\log(\text{price})$ and the predictors are mileage and year. 2

1. **State the problem:** We have age groups of employees and their frequencies. We need to draw a frequency polygon, frequency curve, and histogram with frequency polygon on the s