Question
In: Statistics and Probability
3. Test the null hypothesis that the mean rating of Trump by profs is greater than...
3. Test the null hypothesis that the mean rating of Trump by profs is greater than or equal to the mean rating of Trump by students. Use .10 significance level, a one tail test and the following data:
sample profs students
Mean 21 25
Variance 48 45
number 16 9
Solutions
Expert Solution
| Ho:μ1-μ2 |
|
0 | |
| Ha: μ1-μ2 | < | 0 |
| Profs | students | ||
| x1 = | 21.00 | x2 = | 25.00 |
| s1 = | 6.93 | s2 = | 6.71 |
| n1 = | 16 | n2 = | 9 |
| degree of freedom v= | (n1+n2-2)= | 23.000 | |
| for 0.1 level ,left tail test &23 df, critical t= | 1.319 | ||
| Decision rule : reject Ho if test statistic t<-1.319 | |||
| Pooled Variance Sp2=((n1-1)s21+(n2-1)*s22)/(n1+n2-2)= | 46.9565 | |||
| Point estimate : x1-x2= | -4.0000 | ||
| standard error se =Sp*√(1/n1+1/n2)= | 2.855 | ||
| test stat t =(x1-x2-Δo)/Se= | -1.4010 | ||
| since test statistic falls in rejection region we reject null hypothesis |
| we have sufficient evidence to conclude that mean rating of Trump by profs is less than the mean rating of Trump by students |
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