High School

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------------------------------------------------ Suppose you found a z-statistic of 1.69. If the alternative hypothesis is one-sided, what would be the p-value?

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?