Question

In: Statistics and Probability

School boards in Nova Scotia, on average receive a budget of $623.00 per student from the...

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.

  • State assumptions
  • State the null hypothesis and the alternative hypothesis
  • State the appropriate hypothesis test for each question and determine your critical scores for testing significance at .05
  • Calculate your test statistic making sure you show your formulas
  • Interpret your results using complete sentences indicating is significance was determined

Solutions

Expert Solution

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 .


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