Question

Take it Home: Hypothesis Test for Paired Samples Comparing grocery prices consumer groups often analyze store prices and compare the price of similar items in different stores. They share this information with other consumers or customers.

The data given is a paired sample because they are both the grocery items are the same.

mean of the sample differences ( x bar) = - 0.28

standard deviation of sample differences (s) = 0.31

number of data pairs in sample (n) = 6

null hypothesis is the mean equal to zero

alternative hypothesis the mean is not equal to zero

This is a two tailed test

The criteria is met because we assume the population of the test scores differences is normally distributed

a. Calculate the test statistic for the observed mean of the sample differences. please explain the steps

b. Sketch the t- distribution. Identify the position of the observed test statistic and shade the area that represent the p-value.

c. Use the test statistic to determine the p-value and state the level of significance. please explain the step of how you got to your answer

d. State a conclusion

Answer 1

mean of the sample differences ( x bar) = - 0.28

standard deviation of sample differences (s) = 0.31

number of data pairs in sample (n) = 6

null hypothesis is the mean equal to zero

alternative hypothesis the mean is not equal to zero

This is a two tailed test.

test statistic t = = = -2.212

p-value = 2(P(t<-2.212)) = 0.0779

level of significance = 0.05

Since p-value > alpha we fail to reject H0 and there is no significant evidence that there is a significant difference between the grocery prices of different stores.