Question

1. The table below represents data on a variable of interest collected from a single sample. It is known that the variable of interest has a mean of 10 and a standard deviation of 5 in the general population. A researcher is interested in testing whether the population from which this sample was selected is different from the general population.

				Data
9	7	12	5	6	4	8	11	3	7

1. What are the appropriate hypotheses for this analysis?
2. What is/are the critical value(s) for this test at a 0.05 alpha level?
3. What is the standard error of the mean?
4. What is the observed value of the appropriate test statistic?
5. What is your decision regarding the stated hypotheses?

Answer 1

HYPOTHESIS TEST-

Suppose, corresponding random variable of interest be X.

We have sample values as well as value of population standard deviation (or variance). So, we have to perform one sample z-test.

We have to test for null hypothesis

against the alternative hypothesis

Our test statistic is given by

Here,

Sample size

Sample mean is given by

Population standard deviation

Level of significance

Critical value is given by

[Using R-code 'qnorm(1-0.05/2)']

We reject our null hypothesis if

Here, we observe that

So, we cannot reject our null hypothesis.

ANSWER-

(a)

Null hypothesis is and alternative hypothesis is

(b)

Critical value is

(c)

Standard error of mean is

(d)

Observed value of the appropriate test statistic is

(e)

We observe that

So, we cannot reject our null hypothesis.

Hence, based on the given data we can conclude that there is no significant evidence that the sample mean is different from general population mean.