In: Statistics and Probability
School boards in Nova Scotia, on average receive a budget of $623.00 per student from the provincial government. A random sample of 45 rural schools report that they received on average $605 per student with a standard deviation of $74. Is there a significant difference in the budgets between rural schools and the whole province? (20%)
This question is an example of statistical research using hypothesis testing. You will need to use the 5 step model of hypothesis testing to test for significance at a=.05.
Given that ,
......Population mean
..... Population Standard deviation
n = 45 .....Sample size
.....Sample mean
Step 1:
Assumption :
a) Population standard deviation is known , hence we use Z test .
b)
Since sample size is greater than 30 and Standard deviation is given hence we used Z test .
Here , We want to test ,
Null hypothesis :
.....There is no significant difference in budget between rural schools and the whole province .
v/s
Alternative Hypothesis
......There is significant difference in budget between rural schools and the whole province .
Test statistic is ,
Table value :
( Critical Value)
Decision Rule : If then we reject at 5% level of significance .
Here ,
And
Decision : Here , , Hence we cannot reject at 5% level of significance .
Conclusion : There is no significant difference in budget between rural schools and the whole province .