Question

A middle school is implementing a healthier lunch (low carbs, high protein) program for a variety of reasons, one of which is to decrease office referrals due to behavior. The new menu is used for an entire school year (9 months). The number of office referrals for each month from the previous year is compare to the months of the current year. Has the new menu significantly decreased office referrals? The t-test of related samples was conducted at the .05 level. The Statcrunch results are as follows. (11.5 points)

Paired T statistics

Hypothesis test results:
μ_D : mean of the paired difference between post and pre
H₀ : μ_D = 0
H_A : μ_D < 0

Difference	Sample Diff.	Std. Err.	DF	T-Stat	P-value
post - pre	6.5555553	0.8992452	8	7.2900643	<0.0001

Step 1: Develop Hypotheses:

a.     Independent Variable =                                                   Scale: Categorical       Quantitative (1 pt)

b.    Dependent Variable =                                                     Scale: Categorical       Quantitative   (1 pt)

c.     Circle:     One-tailed       Two-tailed (1 pt)

d.    Alternative hypothesis in sentence form. (1 pt)                                                                                                                                                                                                                                                                                                                                                                                   

e.     Null hypothesis in sentence form. (1 pt)                                                                                                                                       

       

f.     Write the alternative and null hypotheses using correct notation. (1 pt)

                                                  H₁:                                                                H₀:                                                                                                                    

Step 2: Establish significance criteria (.05 pt)

g.     a =

Step 3: Calculate test statistic, effect size, confidence interval, and power (3 pts)

h.    t_calculated =                                                        Level of significance (p) =                                  

i.     Decision:      reject null or                   fail to reject null

       

j.     Calculate effect size =                                                                                             

Step 4: Draw conclusion (2 pts)

k.    Write your conclusion in sentence form including appropriate results notation.

Answer 1

a.     Independent Variable =      Quantitative                 Scale: Ratio

b.    Dependent Variable =          Quantitative               Scale: Ratio

c.     Circle:     One-tailed

d.    Alternative hypothesis in sentence form.

new menu significantly decreased office referrals.That is

There is a decrease  in mean number of office referrals for each month from the previous year compared to the months of the current year.

e.     Null hypothesis in sentence form.

There is no change in mean number of office referrals for each month from the previous year compared to the months of the current year.

f.     Write the alternative and null hypotheses using correct notation.

                                                  H1:μD < 0                                                                H0:          μD = 0

Step 2: Establish significance criteria (.05 pt)

g.     a =0.05

Step 3: Calculate test statistic, effect size, confidence interval, and power (3 pts)

h.    tcalculated =      7.2900643                                                  Level of significance: (p) <0.0001                            

since p less than alpha

0.0001<0.05

p<0.05

Reject null hypothesis

i.     Decision:      reject null hypothesis
Effect size=change in mean/stddev

=6.5555553/(0.8992452*sqrt(12))

= 2.10446

Effect size = 2.10446

Effect size is large

Step 4: Draw conclusion (2 pts)

There is suffcient statistical evidence at 5% level of significance to conlcude that  new menu significantly decreased office referrals.