Question

1. n=49, ? ̅ =8.5, µ=9.2, σ=2.6, α=.01, H₀: μ = 9.2, H₁: μ ≠ 9.2.
   1. Determine z-score __________
   2. Determine p= ____________
   3. Reject or fail to reject H₀ __________

Answer 1

Solution:
Given in the question
Null hypothesis H0: μ = 9.2
Alternate hypothesis Ha: μ ≠ 9.2
This is two tailed hypotehsis
Number of sample (n) = 49
sample mean (Xbar) = 8.5
Population standard deviation (σ) =2.6
Solution(a)
Here we will use Z test as Sample size is large enough and population standard deviation is known, So test statistic Z score can be calculated as
Z-score = (Xbar - μ)/σ/sqrt(n) = (8.5-9.2)/2.6/sqrt(49) = -1.885
Solution(b)
This is two tailed test so from Z table we found p-value = 0.0594
Solution(c)
At alpha = 0.01, we are failed to reject the null hypothesis as p-value is greater than alpha value i.e. (0.0594>0.01).
So we are failed to reject the null hypothesis H0.