Question

A random sample is selected from an approximately normal population with an unknown standard deviation. For each the given set of hypotheses, sample sizes and t-statistics, find the p-value, draw a t-curve and shade the region of which the area the p-value indicates. As it’s not possible to find the precise p-values using a t-table, it suffices to give a range.

(a) H_A : μ > 0.5, n=26, T =2.6

(b) H_A : μ ≠ 0.5, n=26, T = 2.6

(c) H_A : μ < 3, n=18 ,T = −2.2

(d) H_A : μ < 3, n=18, T = 2.2

Answer 1

a)

Right tailed test .

n = 26

df = 26 - 1 = 25

t=2.6

p value=0.0076

b)two tailed test

Right tailed test .

n = 26

df = 26 - 1 = 25

t=2.6

p value=0.0152

c)

Left tailed test .

n = 18

df = 18 - 1 = 17

t=-2.2

p value=0.02095

d)

Left tailed test .

n = 18

df = 18 - 1 = 17

t=2.2

p value=0.02