9. A random sample of n = 12 individuals is selected from a...

9. A random sample of n = 12 individuals is selected from a population with ? = 70, and a treatment is administered to each individual in the sample. After treatment, the sample mean is found to be M = 74.5 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 difference 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 ? = .05.

Transcript

00:01 Hello everyone we are going to solve a question and in this question we are given sample size which is denoted by small and equals to 12 population mean population mean that is mu equals to 70 sample mean that is capital m is equal to 74 .5 and sum of squares that is denoted by double s is equals to 297.

00:42 In this question we have to find three parts and in a part our aim is to find difference between.

00:53 Here we can write it as difference between sample mean and population mean.

01:11 So that means we have to find m minus mu as m as m is 74 .4 .5.

01:18 Minus 70 so from here we have this is equals to 4 .5 which is the answer for a part moving on to the b part in b part our aim is to find the standard error of sample mean standard error of sample mean so the firstly we find the sample variance and the formula for sample variance is equal to, this is noted by s squared, which is equals to s is divided by n minus 1.

02:03 So, s squared is equal to 297 divided by 12 minus 1, which is equals to 297 divided by 11.

02:15 So that means h squared is equals to 27.

02:19 And as we have to find standard error of sample mean, so standard error, here it is error, standard error of sample mean.

02:39 This is defined as s m which is equals to under root h squared divided by n.

02:47 As the value of x s square is 27 so this sm is equal to under root 27 divided by 12 which comes out to be under root 2 .25 and this is equals to 1 .5 so hence sm is equals to 1 .5 is final answer of b part now moving on to the c part in c part our aim is to test whether there is significant effect, whether there is significant effect between population mean and sample mean.

03:51 Two hypothesis that is null hypothesis and alternative.

03:55 Null hypothesis is defined by h0 which is there is no significant difference between population mean and sample mean.

04:21 And we define alternative hypothesis as ha and this is there is difference between population mean and sample mean...

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