Supposed that the z is the test statistics for hypothesis testing, calculate the value of the z for each of the following. Express your answer in 2 decimal places.
13. µ = 8, σ = 4, n = 100, x̄ = 7.2
Answer: Answer
14. µ = 25, σ = 5, n = 90, x̄ = 23.4
Answer: Answer
15. µ = 77, σ = 6, n = 150, x̄ = 78.2
Answer: Answer
16. µ = 8.5, σ = 4, n = 120, x̄ = 7.2
Answer: Answer
17. µ = 20.8, σ = 4, n = 90, x̄ = 21.2
Answer: Answer
18. µ = 31.2, σ = 3, n = 77, x̄ = 32
Answer: Answer
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Step-by-step explanation:
To calculate the value of z for each scenario, we can use the formula:
z = (x̄ - µ) / (σ / √n)
where:
x̄ is the sample mean,
µ is the population mean,
σ is the population standard deviation, and
n is the sample size.
Let's calculate the value of z for each scenario:
13. µ = 8, σ = 4, n = 100, x̄ = 7.2
z = (7.2 - 8) / (4 / √100) = -0.8 / 0.4 = -2
Answer: -2.00
14. µ = 25, σ = 5, n = 90, x̄ = 23.4
z = (23.4 - 25) / (5 / √90) = -1.6 / 0.5916 ≈ -2.706
Answer: -2.71
15. µ = 77, σ = 6, n = 150, x̄ = 78.2
z = (78.2 - 77) / (6 / √150) = 1.2 / 0.4905 ≈ 2.447
Answer: 2.45
16. µ = 8.5, σ = 4, n = 120, x̄ = 7.2
z = (7.2 - 8.5) / (4 / √120) = -1.3 / 0.3651 ≈ -3.563
Answer: -3.56
17. µ = 20.8, σ = 4, n = 90, x̄ = 21.2
z = (21.2 - 20.8) / (4 / √90) = 0.4 / 0.5292 ≈ 0.756
Answer: 0.76
18. µ = 31.2, σ = 3, n = 77, x̄ = 32
z = (32 - 31.2) / (3 / √77) = 0.8 / 0.3429 ≈ 2.33
Answer: 2.33
Please note that the values have been rounded to 2 decimal places as requested.