A machine is set to fill packs with a mean of 50 g; you suspect it underfills. The standard deviation is known to be 2 g. You will weigh a sample of 100 packs and test H₀: μ = 50 against H₁: μ < 50 at α = 0.01. Below which sample mean x̄c will you reject H₀?
A supplier claims that the mean breaking strength of a cable is 75 kN; you suspect it is higher. The standard deviation is known to be 10 kN. You will take a sample of 64 cables and test H₀: μ = 75 kN against H₁: μ > 75 kN at α = 0.05. Above which sample mean x̄c will you reject H₀?
A sample of 100 students has a mean score of 198.2 and a sample standard deviation of 8. Find the test statistic t for H₀: μ = 200.
The mean of a population is claimed to be 80; the population standard deviation is known to be 9. A random sample of 36 observations has a mean of 81.62. Test H₀: μ = 80 against H₁: μ > 80. Find the p-value p.
A sample of 36 measurements has mean 120.5. The population standard deviation is 10. Find the upper limit U of the 99% confidence interval for the mean.
A one-sided z test at α = 0.01 must detect a shift of the mean of 1.5 units with a power of 80%. The standard deviation is 4. Find the minimum sample size n.
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