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 64 packs and test H₀: μ = 120 against H₁: μ < 120 at α = 0.10. Below which sample mean x̄c will you reject H₀?
A machine is supposed to fill bottles with 120 mL on average. The standard deviation is known to be 10 mL. A sample of 36 bottles has a mean of 114.8 mL. Find the test statistic z for H₀: μ = 120.
The mean of a population is claimed to be 120; the population standard deviation is known to be 15. A random sample of 25 observations has a mean of 115.68. Test H₀: μ = 120 against H₁: μ < 120. Find the p-value p.
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 2.73 and the standard deviation of the differences is 9.1. Find the paired test statistic t for H₀: μd = 0.
How large must a sample be so that the 95% confidence interval for a mean has a margin of error of at most 0.5? The standard deviation is 5. Find the smallest sample size n.
In a trial, 75 of 300 patients on treatment A recover, and 22 of 100 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.
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