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 6 kN. You will take a sample of 25 cables and test H₀: μ = 75 kN against H₁: μ > 75 kN at α = 0.10. Above which sample mean x̄c will you reject H₀?
A company claims that a proportion of 0.7 of its customers are satisfied. In a random survey of 200 customers, 122 say they are satisfied. Find the test statistic z for H₀: p = 0.7.
A sample of 16 students has a mean score of 54.8 and a sample standard deviation of 8. Find the test statistic t for H₀: μ = 50.
The mean of a population is claimed to be 80; the population standard deviation is known to be 7.5. A random sample of 25 observations has a mean of 82.82. Test H₀: μ = 80 against H₁: μ > 80. Find the p-value p.
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 20. Find the smallest sample size n.
How large must a sample be so that the 95% confidence interval for a mean has a margin of error of at most 1? The standard deviation is 5. Find the smallest sample size n.
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