A supplier claims that the mean breaking strength of a cable is 200 kN; you suspect it is higher. The standard deviation is known to be 12 kN. You will take a sample of 36 cables and test H₀: μ = 200 kN against H₁: μ > 200 kN at α = 0.05. Above which sample mean x̄c will you reject H₀?
A machine is supposed to fill bottles with 100 mL on average. The standard deviation is known to be 4 mL. A sample of 100 bottles has a mean of 98.76 mL. Find the test statistic z for H₀: μ = 100.
Two teaching methods are compared. Group 1: 5 students, mean score 118.5, standard deviation 7. Group 2: 17 students, mean score 109.1, standard deviation 6.5. 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).
16 employees take a typing test before and after a training course. For each person the difference d = after − before (words per minute) is recorded. The mean difference is 3.42 and the standard deviation of the differences is 7.2. Find the paired test statistic t for H₀: μd = 0.
A sample of 81 measurements has mean 101.2. The population standard deviation is 12. Find the lower limit L of the 90% confidence interval for the mean.
A one-sided z test at α = 0.05 must detect a shift of the mean of 2 units with a power of 95%. The standard deviation is 13. Find the minimum sample size n.
Full step-by-step solutions: practise this topic on examproblems.com.