Question

eBook Find the t-value(s) for each of the following cases. Round your answers to 3 decimal places. Enter negative values as negative number. a. Upper tail area of .025 with 15 degrees of freedom is . b. Lower tail area of .05 with 50 degrees of freedom is C. Upper tail area of .01 with 35 degrees of freedom is d. Where 98% of the area falls between these two t-values with 25 degrees of freedom. e. Where 95% of the area falls between these two t-values with 40 degrees of freedom.

Answer 1

SOLUTION:

From given data,

Find the t-value for each of the following cases.Round your answers to 3 decimal places.

(a) Upper tail area of 0.025 with 15 degree of freedom is

P-value > 0.025 & degree of freedom (df) = 15

The t-critical value for a right-tailed test, for a significance level of α=0.025 is

t-value = 2.131 (From critical t value calculator )

(b) Lower tail area of 0.05 with 50 degree of freedom is

P-value < 0.05 & degree of freedom (df) = 50

The t-critical value for a left-tailed test, for a significance level of α=0.05 is

t-value = −1.676   (From critical t value calculator )

(c) Upper tail area of 0.01 with 35 degree of freedom is

P-value > 0.01 & degree of freedom (df) = 35

The t-critical value for a right-tailed test, for a significance level of α = 0.01 is

t-value = 2.438  (From critical t value calculator )

(d) where 98% of the area falls between these two t-values with 25 degree of freedom

degree of freedom = 25

c = 98% = 98/100 = 0.98

$\alpha$ = 1-c = 1-0.98 = 0.02

$\alpha$/2 = 0.02/2 = 0.01

The t-critical values for a two-tailed test, for a significance level of α=0.02 are

t_{$\alpha$/2,df} = t_0.01,25 = - 2.485  and  t_{$\alpha$/2,df} = t_0.01,25 = +2.485   (From critical t value calculator )

(e) where 95% of the area falls between these two t-values with 40 degree of freedom

degree of freedom = 40

c = 95% = 95/100 = 0.95

$\alpha$ = 1-c = 1-0.95 = 0.05

$\alpha$/2 = 0.05/2 = 0.025

The t-critical values for a two-tailed test, for a significance level of α = 0.05 are

t_{$\alpha$/2,df} = t_0.05,40 = −2.021  and  t_{$\alpha$/2,df} = t_0.05,40 = +2.021   (From critical t value calculator )

Critical t value calculator link:

https://mathcracker.com/t_critical_values#results

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