A supplier claims that the mean breaking strength of a cable is 500 kN; you suspect it is higher. The standard deviation is known to be 5 kN. You will take a sample of 25 cables and test H₀: μ = 500 kN against H₁: μ > 500 kN at α = 0.05. Above which sample mean x̄c will you reject H₀?
A machine is set to fill packs with a mean of 100 g; you suspect it underfills. The standard deviation is known to be 10 g. You will weigh a sample of 25 packs and test H₀: μ = 100 against H₁: μ < 100 at α = 0.10. Below which sample mean x̄c will you reject H₀?
Two teaching methods are compared. Group 1: 7 students, mean score 113, standard deviation 7.5. Group 2: 15 students, mean score 106.2, standard deviation 8.5. Assume equal population variances and use the pooled two-sample t test. Find the test statistic t for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (group 1 minus group 2).
A sample of 25 students has a mean score of 94.72 and a sample standard deviation of 12. Find the test statistic t for H₀: μ = 100.
A sample of 25 measurements has mean 199.9. The population standard deviation is 5. Find the lower limit L of the 99% confidence interval for the mean.
A one-sided z test of H₀: μ = 200 against H₁: μ < 200 is done at α = 0.05 with a sample of 100; the standard deviation is known to be 10. In reality the mean is 196.9. Find the power 1 − β of the test in percent.
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