A machine is set to fill packs with a mean of 100 g; you suspect it underfills. The standard deviation is known to be 15 g. You will weigh a sample of 36 packs and test H₀: μ = 100 against H₁: μ < 100 at α = 0.05. Below 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 10 mL. A sample of 100 bottles has a mean of 102.4 mL. Find the test statistic z for H₀: μ = 100.
A sample of 25 students has a mean score of 95.8 and a sample standard deviation of 15. Find the test statistic t for H₀: μ = 100.
The mean of a population is claimed to be 100; the population standard deviation is known to be 24. A random sample of 144 observations has a mean of 95.84. Test H₀: μ = 100 against H₁: μ < 100. Find the p-value p.
A one-sided z test at α = 0.05 must detect a shift of the mean of 2.5 units with a power of 80%. The standard deviation is 18. Find the minimum sample size n.
How large must a sample be so that the 90% confidence interval for a mean has a margin of error of at most 3? The standard deviation is 4. Find the smallest sample size n.
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