Hypothesis Testing: One-Sample z-Tests & t-Tests (University)
Free printable university statistics worksheet on one-sample hypothesis tests: state H0/Ha, compute the z or t statistic, find the p-value or critical value, and decide at the significance level. Problems are generated from a known true mean so the correct decision is determinate.
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Probability & Statistics · Math worksheet
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Math
Hypothesis Testing: One-Sample z-Tests & t-Tests
State H0 and Ha, compute the test statistic z = (xbar - mu0)/(sigma/sqrt(n)) or t = (xbar - mu0)/(s/sqrt(n)), find the p-value (z-tests) or compare with the critical value (t-tests), and decide at the given alpha.
- 1.The claimed mean of the fill volume of a bottling machine (mL) is 500, with known population standard deviation 6. A random sample of n = 36 gives sample mean 496.1. Test H0: mu = 500 against Ha: mu not equal to 500 at significance level alpha = 0.05. Give the z test statistic (2 dp), the p-value (4 dp), and the decision.
- 2.The claimed mean of the fuel economy of a car model (km/L) is 16. The population standard deviation is unknown; a random sample of n = 20 gives sample mean 17.7 and sample standard deviation 1.6. Test H0: mu = 16 against Ha: mu not equal to 16 at alpha = 0.05 using the t-distribution with df = 19. Give the t test statistic (2 dp), the critical value, and the decision.
- 3.The claimed mean of the daily output of a solar panel model (kWh) is 24, with known population standard deviation 3. A random sample of n = 49 gives sample mean 24.7. Test H0: mu = 24 against Ha: mu not equal to 24 at significance level alpha = 0.05. Give the z test statistic (2 dp), the p-value (4 dp), and the decision.
- 4.The claimed mean of the fuel economy of a car model (km/L) is 16. The population standard deviation is unknown; a random sample of n = 12 gives sample mean 15.9 and sample standard deviation 1.5. Test H0: mu = 16 against Ha: mu not equal to 16 at alpha = 0.05 using the t-distribution with df = 11. Give the t test statistic (2 dp), the critical value, and the decision.
- 5.The claimed mean of the reaction time of trained operators (ms) is 250, with known population standard deviation 15. A random sample of n = 36 gives sample mean 250. Test H0: mu = 250 against Ha: mu less than 250 at significance level alpha = 0.05. Give the z test statistic (2 dp), the p-value (4 dp), and the decision.
- 6.The claimed mean of the battery life of a laptop model (hours) is 10. The population standard deviation is unknown; a random sample of n = 16 gives sample mean 9.9 and sample standard deviation 1.3. Test H0: mu = 10 against Ha: mu not equal to 10 at alpha = 0.01 using the t-distribution with df = 15. Give the t test statistic (2 dp), the critical value, and the decision.
- 7.The claimed mean of the fill volume of a bottling machine (mL) is 500, with known population standard deviation 6. A random sample of n = 100 gives sample mean 497.8. Test H0: mu = 500 against Ha: mu not equal to 500 at significance level alpha = 0.05. Give the z test statistic (2 dp), the p-value (4 dp), and the decision.
- 8.The claimed mean of the mass of cereal boxes from a production line (g) is 750. The population standard deviation is unknown; a random sample of n = 9 gives sample mean 761.5 and sample standard deviation 10.9. Test H0: mu = 750 against Ha: mu greater than 750 at alpha = 0.05 using the t-distribution with df = 8. Give the t test statistic (2 dp), the critical value, and the decision.
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