Hello, I need help with the word problem

Question

1.71) Laughter among deaf signers. The Journal of Deaf Studies and Deaf Education (Fall 2006) published an article on vocalized laughter among deaf users of American sign language (ASL). In videotaped ASL conversations among deaf participants, 28 laughed at least once. The researchers wanted to know if they laughed more as speakers (while signing) or as audience members (while listening). For each of the 28 deaf participants, the number of laugh episodes as a speaker and the number of laugh episodes as an audience member was determined. One goal of the research was to compare the mean number of laugh episodes of speakers and audience members. 

(a) Explain why the data should be analyzed as a paired difference experiment. 

(b) Identify the study’s target parameter. 

(c) The study yielded a sample mean of 3.4 laughter episodes for speakers and a sample mean of 1.3 laughter episodes as an audience. Is this sufficient evidence to conclude that the population means are different? Explain. 

(d) A paired difference t-test resulted in t = 3.14 and p-value < .01. Interp study, the VDOT provided crash data both before and after installation of red light cameras at several intersections. The data (measured as the number of crashes caused by red light running per intersection per year) for 13 intersections in Fairfax County, Virginia, are given in the table. Analyze the data for the VDOT. What do you conclude

Answer 1

a) This data should be analyzed as paired difference data because you have 1 sample (28 deaf participants) with 2 observations for each participant (# laughs when signing and # laughs when "listening."

b)The target parameter is µ_d = the true mean difference (signing - listening) in the number of laughter episodes for all deaf individuals when signing vs listening.

c) The sample difference, d-bar, is 3.4 - 1.3 = 2.1. This is evidence of a difference since this number is not zero; however, without information on the variation (standard deviation) of the individual differences, I cannot determine if this is sufficient evidence to conclude that µ_d is not zero.

d) I will assume that all conditions for inference are met and that the paired data was #crashes before the red light was installed - # crashes after the red light was installed. I also assume that the hypotheses are H₀: µ_d = 0 (there is no difference in the number of crashes after the red lights were installed) vs H_a: µ_d >0 (the number of crashes decreased after installation of the red lights). With these assumptions, since the p-value of <0.01 is less than 0.05, I can reject the null hypothesis and conclude that the installation of red lights at these intersections reduced the number of crashes.

Note: the wording of this problem is "off." How can you have a crash involving running a red light before the red light was installed.

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