Question 2 - A state legislator wants to determine whether her performance ratin
ID: 3061815 • Letter: Q
Question
Question 2 - A state legislator wants to determine whether her performance rating (0-100) has changed from last year to this year. The following table shows the legislator's performance ratings from the same 16 randomly selected voters for last year and this year. Befor or 054 78 84 91 25 50 65 68 8175 45 62 79 58 63 After 51 4365 55 80 35 35 50 75 70 73 45 45 80 48 55 Part A Can we conclude that the legislator's performance rating has significantly changed? a. 12 marks] State the null and alternative hypotheses. You must define all notations used in the hypotheses.Explanation / Answer
## By using r command:
> Before=c(60,54,78,84,91,25,50,65,68,81,75,45,62,79,58,63)
> Before
[1] 60 54 78 84 91 25 50 65 68 81 75 45 62 79 58 63
> After= c(41,43,65,55,80,35,35,50,75,70,73,45,45,80,48,55)
> After
[1] 41 43 65 55 80 35 35 50 75 70 73 45 45 80 48 55
> t.test(Before,After,paired=T)
Paired t-test
data: Before and After
t = 3.5597, df = 15, p-value = 0.002852
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
3.585946 14.289054
sample estimates:
mean of the differences
8.9375
a)
Null Hypothesis: There is no significant difference between before and after mean performance ratings.
Vs
Alternative Hypothesis: There is a significant difference between before and after mean performance ratings.
b) t statistics = 3.5597, p-value = 0.002852
c) At 5% level of significance Pvalue 0.0029 indicates the rejection of null hypothesis. Hence the legislators performance rating is improved from last year to this year.
d) The 95% confidence interval is given by
3.585946, 14.289054
e) Since the 95% confidence interval does not contains zero, we say that the legislators performance rating is improved from last year to this year.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.