1.Easy
A company claims that a proportion of 0.75 of its customers are satisfied. In a random survey of 100 customers, 64 say they are satisfied. Find the test statistic z for H₀: p = 0.75.
p₀ = 0.75n = 100x = 64
z =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A machine is set to fill packs with a mean of 120 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 = 120 against H₁: μ < 120 at α = 0.10. Below which sample mean x̄c will you reject H₀?
μ₀ = 120 gσ = 6 gn = 64α = 0.10
x̄c = g
3.Medium
A sample of 64 students has a mean score of 499.1 and a sample standard deviation of 5. Find the test statistic t for H₀: μ = 500.
μ₀ = 500x̄ = 499.1s = 5n = 64
t =
4.Medium
7 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 −4.38 and the standard deviation of the differences is 6.1. Find the paired test statistic t for H₀: μd = 0.
n = 7d̄ = −4.38sd = 6.1
t =
5.Hard
In a trial, 90 of 300 patients on treatment A recover, and 41 of 120 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.
x₁ = 90n₁ = 300x₂ = 41n₂ = 120
z =
6.Hard
How large must a sample be so that the 95% confidence interval for a mean has a margin of error of at most 2? The standard deviation is 5. Find the smallest sample size n.
σ = 5E = 295%
n =
Answer key
- 1. z = −2.54
- 2. x̄c = 119 g
- 3. t = −1.44
- 4. t = −1.9
- 5. z = −0.8327
- 6. n = 25
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