Question

I have to work this problem out using a ti-84 calculator and have no idea how to.

A survey of 47 people was conducted to compare their self-reported height to their actual height. The difference between reported height and actual height was calculated.

You're testing the claim that the mean difference is greater than 1.4.

From the sample, the mean difference was 1.6, with a standard deviation of 0.5.

Calculate the test statistic, rounded to two decimal places

Answer 1

This is a paired -t test, since if X denotes each individuals self-reported height and Y denotes their actual height, so (X,Y) will be dependent on each other, Define Z=X-Y,for each person and define  

Hypothesis to be tested:

Under the null hypothesis,

So test statistic to test the claim =

To find critical value :

In your calculator, press 2nd-> distr-> invT -> Enter -> Input your probability of confidence, degrees for freedom, for example - type (0.95,46)-> enter.

so, at level of confidence 0.05, critical value = 1.67866

Since, T> critical value we reject the null hypothesis at 0.05 level of confidence.