📊 statistics

1. Let's state the problem: We want to know when a researcher should use a one-sample t-test instead of a z-test. 2. A one-sample z-test is typically used when the population mean

1. We are given a sample size $n = 15$ and the sum of squares $SS = 196$. We need to find the sample variance $s^2$ and the estimated standard error $s_m$. 2. The formula for the s

1. **State the problem:** We have a list of days absent from work for 30 workers. We need to prepare a frequency table showing how many workers have each number of absent days. 2.

1. The problem asks us to calculate the mean temperature from the following values: 12°C, 11°C, 8°C, 13°C, and 16°C. 2. To find the mean, we sum all the temperatures and then divid

1. The problem asks us to calculate the mean (average) volume of gas released from the given data. 2. The volumes given are: $32, 35, 28, 30, 30$ cm$^3$.

1. **State the problem:** Calculate the mean (average) of the values 8, 9, 7, 2, and 4. 2. **List the values:** The numbers are 8, 9, 7, 2, and 4.

1. **Problem:** For test $H_0: \mu=100$ vs $H_1: \mu>100$, sample $z=2.15$. Find the p-value. 2. This is a right-tailed test so p-value = $P(Z \geq 2.15)$.

1. The problem asks for the most effective graph type to display proportions of different types of waste in a landfill. 2. A pie chart is ideal for showing proportions or percentag

1. **State the problem:** We are given a pie chart representing 120 gym members' daily exercise amounts. The chart sections are: - 162° for "< 30 minutes"

1. Find the mode for frequency distribution: Given marks intervals and frequencies: 0-10(7), 10-20(14), 20-30(13), 30-40(12), 40-50(20), 50-60(11), 60-70(15), 70-80(8).

1. Problem 27: Given mode = 55, find $x$ in frequency distribution: | Class | 0-15 | 15-30 | 30-45 | 45-60 | 60-75 | 75-90 |

1. Stating the problem: We need to find what percentage of Graduates joined the HR team last year. 2. Collect the data:

1. The problem asks for the difference between the highest and lowest marketing campaign reach percentages for Poland. 2. The reported percentages for Poland are 80%, 65%, 49%, and

1. **State the problem:** We need to identify which mistake Katie made in her stem-and-leaf diagram for the caterpillar lengths.

1. The problem requires us to organize the given weights (kg) into an ordered stem-and-leaf diagram. 2. First, list all weights in order from smallest to largest:

1. We are given a set of weights in kilograms: $0.3, 0.4, 0.9, 0.1, 0.2, 1.0, 0.2, 1.1, 0.4, 1.3, 1.6, 1.1, 2.3, 0.2$. 2. Our goal is to create an ordered stem-and-leaf diagram. Th

1. The problem is to fill in the missing row for the stem-and-leaf diagram showing the number of visitors to a cafe each day. 2. We are given visitor numbers: 102, 115, 91, 113, 94

1. **Stating the problem:** We are given a frequency polygon representing heights of members in a netball club. Our task is to estimate the mean height to 1 decimal place. 2. **Ide

1. The problem asks for the median of the numbers: 12, -6, -9, 1, -13. 2. To find the median, first arrange the numbers in ascending order.

1. مسأله: بررسی تفاوت معنی دار در میانگین نمرات سه گروه درمانی A، B، و C با استفاده از تحلیل واریانس (ANOVA) در سطح معنی داری ۵٪. 2. داده‌ها:

1. مسئله: بررسی اینکه آیا تفاوت معنادار آماری بین سه روش درمانی A, B, و C در کاهش میزان افسردگی وجود دارد یا خیر بر اساس نمرات داده شده با سطح معنی داری 0.05. 2. داده‌ها: