Question

a through C. formula process please thank you  

204 9. A random sample of n = 12 individuals is selected from a population with u = 70. and a treatment is administered to each individual in the sample. Antes treatment, the sample mean is found to be M = 14. with SS = 297. a. How much difference is there between the mean for the treated sample and the mean for the original population? (Note: In a hypothesis test, this value forms the numerator of the t statistic.) b. If there is no treatment effect, how much differ- ence is expected just by chance between the sample mean and its population mean? That is, find the standard error for M. (Note: In a hypothesis test, this value is the denominator of the t statistic.) c. Based on the sample data, does the treatment have a significant effect? Use a two-tailed test with a = .05.

Answer 1

Answer:

Given,

n = 12

mean = 70

M = 74.5

SS = 297

s^2 = SS/(n-1)

= 297/(12-1)

= 297/11

s^2 = 27

degree of freedom = n - 1

= 12 - 1

= 11

a)

To give difference b/w population mean & sample mean

Difference = M - mean

= 74.5 - 70

= 4.5

b)

To give the standard error

consider,

Standard error = sqrt(s^2 / n)

substitute values

= sqrt(27/12)

SE = 1.5

c)

Here it is two tailed test

alpha = 0.05

test statistic = (xbar - mu) / SE

substitute values

= (74.5 - 70) / 1.5

= 4.5 / 1.5

test statistic = 3

Here t value corresponding to t(0.05/2 , 11) is 2.201

We observed that the calculated test statistic > critical value , so we reject null hypothesis Ho.

So there is a significant effect.