Question

# A sample is randomly selected from a population with a mean of μ = 50, and...

A sample is randomly selected from a population with a mean of μ = 50, and a treatment is administered to the individuals in the sample. After treatment, the sample is found to have a mean of M = 56 with a standard deviation of s = 8. If there are n = 4 individuals in the sample, are the data sufficient to reject Ho and conclude that the treatment has a significant effect using a two-tailed test with = .05? (Use/round to 3 decimal places.)

t-critial= +/-

t=

Do you accept or reject the null hypothesis based on these results?

Solution :

Given that ,

= 50

M = 56

s = 8

n = 4

The null and alternative hypothesis is ,

H0 :   = 50

Ha :    50

This is the two tailed test .

df = n - 1 = 4 - 1 = 3

= 0.05

t,df = t0.05,3 = +/-3.182

The critical value = +/-3.182

Test statistic = t

= (M - ) / s / n

= ( 56 - 50) / 8 / 4

= 1.5

The test statistic = 1.5

1.5 < +/-3.182

test statistic < critical value

Reject the null hypothesis .

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