Statistical Inference Worksheets Grade 11

1. Matiu is a Grade 11 student investigating whether a new online learning platform improves student performance in mathematics. He collects a random sample of 40 students who used the platform for one semester and finds their average final exam score is 76.4. The school's historical average final exam score for all students (without the platform) is 72.0 with a known population standard deviation of 8.2. Matiu wants to conduct a hypothesis test at a significance level of α = 0.05 to determine if the platform leads to higher scores. Calculate the z-test statistic for this hypothesis test, rounded to two decimal places.
2. A university is studying whether a new study method improves test scores. They randomly select 64 students who use the method and find their average score is 82 with a standard deviation of 12. The historical average score for all students is 78. The researchers conduct a hypothesis test at α = 0.05 significance level to determine if the new method leads to higher scores. Calculate the test statistic for this hypothesis test.
3. A scatter plot displays the relationship between daily temperature in °C (x) and ice cream sales in dollars (y) for 60 days. The least squares regression line is calculated as ŷ = 15.2x + 120. A residual plot shows points randomly scattered around zero with no discernible pattern. If the temperature reaches 32°C, what total ice cream sales does the regression model predict?

…and 3 more problems

1. Tane is a marine biologist studying the average length of a specific species of fish in a large lake. He catches a random sample of 49 fish and measures their lengths. The sample mean length is 42.5 cm with a sample standard deviation of 9.8 cm. Tane wants to estimate the true mean length of this fish species in the entire lake. What is the margin of error for a 95% confidence interval for the population mean? (Use t* = 2.01 for 48 degrees of freedom.)
2. A scatter plot displays the relationship between daily exercise time (x, in minutes) and resting heart rate (y, in beats per minute) for 60 adults. The least squares regression line is calculated as ŷ = -0.35x + 72. A residual plot shows points randomly scattered around zero with no clear pattern. If an adult exercises for 45 minutes daily, what resting heart rate does the regression model predict?
3. Kaia is an environmental scientist studying the health of a native forest. She collects a random sample of 49 trees and measures their trunk diameters (in cm). The sample mean diameter is 31 cm with a sample standard deviation of 7 cm. Kaia wants to estimate the true mean trunk diameter of all trees in the forest with 95% confidence. Calculate the margin of error for this estimate, and then state the 95% confidence interval for the population mean trunk diameter.

…and 3 more problems

1. Mere is investigating whether the average daily screen time for teenagers in her city is different from the national average of 5.5 hours. She surveys a random sample of 64 teenagers and finds that their mean daily screen time is 6.2 hours with a standard deviation of 1.6 hours. Using a 95% confidence level, calculate the margin of error for her estimate and interpret what this confidence interval suggests about the population mean.
2. A university is studying whether a new study technique improves test scores. They randomly select 64 students and find the mean improvement is 8.2 points with a standard deviation of 12 points. Using a significance level of α = 0.05, test the hypothesis H₀: μ = 0 versus H₁: μ > 0. What is the calculated test statistic value? Round your answer to two decimal places.
3. P(Z > 1.28) = ?

…and 4 more problems