Question

The following information is given for a one-sample t test: H0: μ = 100; HA: μ < 100 Sample statistics: x̅= 95; s = 12.42 Value of the test statistic: t = –1.80 (a) Determine the sample size, n. (b) At a significance level α = 0.05, would your decision be to reject H0 or fail to reject H0?

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 100

H_a : < 100

= 95

= 100

s = 12.42

t = -1.80

(a)

Test statistic = t

= ( - ) / s / n

n = t * s / ( ( - )

= (-1.80 * 12.42 ) / (95 - 100)

= -22.356 / - 5

n = 4.4712

n = 20

df = n - 1 = 20 - 1 = 19

= 0.05

P-value = 0.0439

P-value <

Reject the null hypothesis (H0) .