Question

Calculate the critical value, test Ho: and state the final decisions for each of the following cases.

4 (a)
Level of significance = 5% 2-tailed test
Sample size = 50
Population mean = 750
Population standard deviation = 60 Sample mean = 600

4 (b)
Level of significance = 5%

1-tailed test
Sample standard deviation = 25

Sample size = 45 Population mean = 290 Sample mean = 390

Answer 1

a)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 750
Alternative Hypothesis, Ha: μ ≠ 750

Rejection Region
This is two tailed test, for α = 0.05
Critical value of z are -1.96 and 1.96.
Hence reject H0 if z < -1.96 or z > 1.96

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (600 - 750)/(60/sqrt(50))
z = -17.68

P-value Approach
P-value = 0
As P-value < 0.05, reject the null hypothesis.

2)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 290
Alternative Hypothesis, Ha: μ > 290

Rejection Region
This is right tailed test, for α = 0.05 and df = 44
Critical value of t is 1.68.
Hence reject H0 if t > 1.68

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (390 - 290)/(25/sqrt(45))
t = 26.83

P-value Approach
P-value = 0
As P-value < 0.05, reject the null hypothesis.