10. Hypothesis Testing for Two Samples

In Problem 3, assume that the paired differences come from a population that is normally distributed. 

a. Compute di=Xi−Yi for each pair of data.  

McDonald’s versus Wendy’s A student wanted to determine whether the wait time in the drive-thru at McDonald’s differed from that at Wendy’s. She used a random sample of 30 cars at McDonald’s and 27 cars at Wendy’s and obtained these results:  

c. Is there a difference in wait times at each restaurant’s drive-thru? Use the α=0.1 level of significance.  

Note: The sample size for Wendy’s is less than 30. However, the data do not contain any outliers, so the Central Limit Theorem can be used. 

a. Determine dᵢ = Xᵢ - Yᵢ for each pair of data.

Naughty or Nice? An experiment was conducted in which 16 ten-month-old babies were asked to watch a climber character attempt to ascend a hill. On two occasions, the baby witnesses the character fail to make the climb. On the third attempt, the baby witnesses either a helper toy push the character up the hill, or a hinderer toy preventing the character from making the ascent. The helper and hinderer toys were shown to each baby in a random fashion for a fixed amount of time. In Problem 41 from Section 10.2, we learned that, after watching both the helper and hinderer toy in action, 14 of 16 ten-month-old babies preferred to play with the helper toy when given a choice as to which toy to play with. A second part of this experiment showed the climber approach the helper toy, which is not a surprising action, and then alternatively the climber approached the hinderer toy, which is a surprising action. The amount of time the ten-month-old watched the event was recorded. The mean difference in time spent watching the climber approach the hinderer toy versus watching the climber approach the helper toy was 1.14 seconds with a standard deviation of 1.75 second. Source: J. Kiley Hamlin et al., “Social Evaluation by Preverbal Infants,” Nature, Nov. 2007.  

c. What do you think the results of this experiment imply about 10-month-olds’ ability to assess surprising behavior?

[NW] [DATA] Muzzle Velocity The following data represent the muzzle velocity (in feet per second) of rounds fired from a 155-mm gun. For each round, two measurements of the velocity were recorded using two different measuring devices, with the following data obtained:

a. Why are these matched-pairs data?

Reaction Time In an experiment conducted online at the University of Mississippi, study participants are asked to react to a stimulus. In one experiment, the participant must press a key on seeing a blue screen and reaction time (in seconds) to press the key is measured. The same person is then asked to press a key on seeing a red screen, again with reaction time measured. The results for six randomly sampled study participants are as follows:

c. Is the reaction time to the blue stimulus different from the reaction time to the red stimulus at the α=0.01 level of significance? Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.

[DATA] Invest in Education Go to www.pearsonhighered.com/sullivanstats to obtain the data file 12_3_17. The variable “Cost” represents the four-year cost including tuition, supplies, room and board, the variable “Annual ROI” represents the return on investment for graduates of the school—essentially how much you would earn on the investment of attending the school. The variable “Grad Rate” represents the graduation rate of the school.

a. In Problem 49 from Section 4.1, a scatter diagram between “Cost” and “Grad Rate” treating “Cost” as the explanatory variable suggested a positive association between the two variables. Treating “Cost” as the explanatory variable, x, test whether a negative association exists between the cost and annual ROI for graduates of four-year schools at the alpha = 0.01 level of significance. Normal probability plots suggest the residuals are normally distributed.