Question

1. For a random sample of 36 data pairs, the sample mean of the differences was 0.8. The sample standard deviation of the differences was 2. Test the claim that the population mean of the differences is different than 0 using alpha at .05.
   1. State the null and alternative hypotheses (.5 points)

2. What is the formula you will use? (.5 points)

3. Identify all variables and corresponding values from the formula. Calculate the test statistic. (2 points)

4. Sketch the distribution, label the critical value(s), shade the critical region(s), and plot the calculated test statistic. (1.5 points)

5. Interpret your result. (1.5 points)

Answer 1

(A) Given claim is that the population mean of the differences is different than 0

So, Null hypothesis:- difference for the population means is equal to 0

Alternate hypothesis:- difference for the population means is not equal to 0

(B) Population standard deviation is unknown, so we will use t distribution for hypothesis testing

Formula used is

(C) sample mean difference is 0.80 and standard deviation of the difference is 2

sample size is n = 36

this implies

(D) degree of freedom = n-1= 36- 1 =35

using t distribution table, df = 35 and significance level of 0.05

t critical value = 2.030

t is denoting the calculated statistics value.

Blank area is denoting the null value area, where we fail to reject the null hypothesis

(E) Since the t calculated value falling outside the t critical value area, therefore, rejecting the null hypothesis

Conclusion:- there is sufficient evidence to conclude that the difference is not equal to 0