A machine is set to fill packs with a mean of 120 g; you suspect it underfills. The standard deviation is known to be 2 g. You will weigh a sample of 25 packs and test H₀: μ = 120 against H₁: μ < 120 at α = 0.05. Below which sample mean x̄c will you reject H₀?
A machine is supposed to fill bottles with 200 mL on average. The standard deviation is known to be 4 mL. A sample of 49 bottles has a mean of 198.7 mL. Find the test statistic z for H₀: μ = 200.
The mean of a population is claimed to be 100; the population standard deviation is known to be 15. A random sample of 100 observations has a mean of 98.65. Test H₀: μ = 100 against H₁: μ ≠ 100. Find the p-value p.
A sample of 49 students has a mean score of 44.43 and a sample standard deviation of 15. Find the test statistic t for H₀: μ = 50.
A one-sided z test at α = 0.01 must detect a shift of the mean of 2 units with a power of 90%. The standard deviation is 9. Find the minimum sample size n.
In a trial, 60 of 150 patients on treatment A recover, and 132 of 300 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.
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