Statistical Inference Worksheets Grade 11

1. H₀: μ = 120, H₁: μ ≠ 120, sample mean = 124.5, σ = 15, n = 64, α = 0.05; z = ?
2. A nutrition researcher is studying the relationship between daily fruit consumption and blood pressure levels. After collecting data from 180 adults, she calculates a correlation coefficient of r = -0.42 between fruit servings and systolic blood pressure. She wants to test if this correlation is statistically significant at α = 0.05. What is the appropriate null hypothesis for this test?
3. Mere is investigating whether the average weekly screen time for Grade 11 students at her school exceeds the national average of 24 hours. She surveys a random sample of 64 students and finds a sample mean of 26.8 hours with a sample standard deviation of 8 hours. Using a significance level of α = 0.05, test the claim that the true mean weekly screen time for students at her school is greater than 24 hours. What is the calculated test statistic? Round your answer to two decimal places.

…and 3 more problems

1. P(Z > 1.96) = ?
2. Emma surveys a random sample of 40 students and finds the mean amount of weekly screen time is 15 hours with a standard deviation of 5 hours. Calculate the 95% confidence interval for the population mean weekly screen time (use z* = 1.96).
3. Emma, a Grade 11 student, is investigating whether the average amount of time students at her high school spend on homework each night is different from the national average of 90 minutes. She surveys a random sample of 40 students and finds that the mean homework time for her sample is 85 minutes, with a standard deviation of 20 minutes. Calculate the test statistic (t-value) for a hypothesis test to determine if the school's average homework time differs from the national average. Round your answer to two decimal places.

…and 3 more problems

1. A sample of 225 students at a large university has a mean GPA of 3.12 with a standard deviation of 0.48. Construct a 95% confidence interval for the population mean GPA. (Use z* = 1.96)
2. Olivia, a researcher at a health institute, wants to estimate the average number of hours per week that Grade 11 students spend on extracurricular activities. She surveys a random sample of 49 students and finds that the sample mean is 11 hours with a sample standard deviation of 3 hours. Based on this sample, calculate a 95% confidence interval for the population mean number of hours per week spent on extracurricular activities by all Grade 11 students. Then, interpret what this interval tells us about the population mean.
3. A sample of 144 students has a mean GPA of 3.12 with a standard deviation of 0.48. Construct a 99% confidence interval for the population mean GPA. (Use z* = 2.576)

…and 4 more problems