Elena Martin is campaigning for the city council. She has two types of lawn signs to distribute: large ones and small ones. She wonders if the size of the sign affects residents' willingness to display the signs on their property. Early in the campaign, her staff obtains a list of homeowners in each of the city's 10 voting districts who are registered in her political party and presumably not averse to advertising their support for her. The staff randomly selects homeowners in each of the 10 districts, to some of whom they send large signs and to others, small signs. Two weeks later, staff members drive by each home to which they sent the signs to record whether or not the sign is being displayed. Here are the percentages of homes displaying the signs in each district:
Large Sign Small Sign
34.......................................... 41
41.......................................... 44
30.......................................... 36
32.......................................... 38
28.......................................... 29
31.......................................... 47
40.......................................... 49
27.......................................... 39
36.......................................... 43
22.......................................... 37
a. Is the research hypothesis in this study directional or non directional?
b. State the research hypothesis.
c. Calculate t and compare it with the tabled critical t at the .01 a level. Can you reject the null hypothesis?