Answer :
a. The p - value if the alternative hypothesis is μ > 5 is 0.0455.
b. The p - value if the alternative hypothesis is μ < 5 is 0.9545.
c. The p - value if the alternative hypothesis is μ ≠ 5 is 0.0910.
Given that,
Test Statistic -
z = 1.69
The objective is to find the p-value at the different alternative hypothesis.
a. We have to find the p - value if the alternative hypothesis is μ > 5.
For μ > 5
Compute p - value
P- value = P(Z > 1.69)
= 1 - P(Z ≤ 1.69)
= 1 - 0.9545 [using standard normal table ]
= 0.0455
Therefore, The p - value if the alternative hypothesis is μ > 5 is 0.0455.
b. We have to find the p - value if the alternative hypothesis is μ < 5.
For μ < 5
Compute p - value
P- value = P(Z < 1.69)
= Φ(1.69)
= 0.9545 [using standard normal table ]
Therefore, The p - value if the alternative hypothesis is μ < 5 is 0.9545.
c. We have to find the p - value if the alternative hypothesis is μ ≠ 5.
For μ ≠ 5
Compute p - value
P- value = 2 × P(Z > |1.69|)
= 2 × P(Z > |1.69|)
= 2 × [1 - P(Z ≤ |1.69|) ]
= 2 × [ 1 - 0.9545] [using standard normal table ]
= 0.0910
Therefore, The p - value if the alternative hypothesis is μ ≠ 5 is 0.0910.
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The question is incomplete the complete question is -
Suppose you found a z-statistic of 1.69.
a. If the alternative hypothesis is μ > 5, what would be the p-value?
b. If the alternative hypothesis is μ < 5, what would be the p-value?
c. If the alternative hypothesis is μ ≠ 5, what would be the p-value?
