t test p-value solutions

Ho: µ ≥ 15

Ha: µ < 15

n = 10, xbar = 7.3, s = 9.2

t = -2.6467

P-value = P(t < -2.6467) based on 9 degrees of freedom

1% critical value = -2.821, 2.5% critical value = -2.262

1% < p-value < 2.5%

α = 5% -> reject Ho

α = 1% -> do not reject Ho

No α -> Inconclusive

Ho: µ = 15

Ha: µ ≠ 15

n = 16, xbar = 10.6, s = 9.2

t = -1.913

P-value =2 P(t > 1.913) based on 15 degrees of freedom

2.5% critical value = 2.131, 5% critical value = 1.753

2.5% <P(t > 1.913) < 5%

5% < P-value < 10%

α = 5% -> do not reject Ho

α = 10% -> reject Ho

No α -> Inconclusive

Ho: µ = 15

Ha: µ ≠ 15

n = 7, xbar = 29.6, s = 9.2

t = 4.1987

P-value =2 P(t > 4.1987) based on 6 degrees of freedom

0.5% critical value = 3.707

P(t > 4.1987) < 0.5%

P-value < 1%

α = 5% -> reject Ho

No α -> reject Ho

Ho: µ = 15

Ha: µ ≠ 15

n = 22, xbar = 17.2, s = 9.2

t = 1.1216

P-value =2 P(t > 1.1216) based on 21 degrees of freedom

10% critical value = 1.323

P(t > 1.913) > 10%

P-value > 20%

α = 5% -> do not reject Ho

No α -> do not reject Ho