A supplier claims that the mean breaking strength of a cable is 100 kN; you suspect it is higher. The standard deviation is known to be 6 kN. You will take a sample of 36 cables and test H₀: μ = 100 kN against H₁: μ > 100 kN at α = 0.01. Above which sample mean x̄c will you reject H₀?
A machine is set to fill packs with a mean of 50 g; you suspect it underfills. The standard deviation is known to be 3 g. You will weigh a sample of 25 packs and test H₀: μ = 50 against H₁: μ < 50 at α = 0.05. Below which sample mean x̄c will you reject H₀?
20 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 1.05 and the standard deviation of the differences is 1.3. Find the paired test statistic t for H₀: μd = 0.
A sample of 64 students has a mean score of 502.1 and a sample standard deviation of 10. Find the test statistic t for H₀: μ = 500.
A one-sided z test of H₀: μ = 100 against H₁: μ < 100 is done at α = 0.10 with a sample of 100; the standard deviation is known to be 25. In reality the mean is 95.5. Find the power 1 − β of the test in percent.
A sample of 16 measurements has mean 87.5. The population standard deviation is 20. Find the lower limit L of the 90% confidence interval for the mean.
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