A machine is set to fill packs with a mean of 75 g; you suspect it underfills. The standard deviation is known to be 6 g. You will weigh a sample of 64 packs and test H₀: μ = 75 against H₁: μ < 75 at α = 0.10. Below which sample mean x̄c will you reject H₀?
A machine is supposed to fill bottles with 75 mL on average. The standard deviation is known to be 12 mL. A sample of 36 bottles has a mean of 76.4 mL. Find the test statistic z for H₀: μ = 75.
A sample of 25 students has a mean score of 92.8 and a sample standard deviation of 20. Find the test statistic t for H₀: μ = 100.
A sample of 36 students has a mean score of 77 and a sample standard deviation of 10. Find the test statistic t for H₀: μ = 75.
A one-sided z test of H₀: μ = 100 against H₁: μ < 100 is done at α = 0.10 with a sample of 25; the standard deviation is known to be 5. In reality the mean is 97.1. Find the power 1 − β of the test in percent.
A sample of 49 measurements has mean 121.7. The population standard deviation is 8. Find the upper limit U of the 90% confidence interval for the mean.
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