Question

For the following, Use the five-step approach to hypothesis testing found on page 8-16. It states. You can use excel to compute the data or you can do it by hand. The youtube videos provided in the links will walk you through the steps to complete the following problems.

1. State the hypothesis and identify the claim.

H0:

H1:

2. Use a Pearson Correlation
3. Compute the test Value It will be a correlation
4. Make a decision to reject or fail to reject the null hypothesis.
5. Summarize the results

Problem #3 You are a researcher who wants to know if there is a relationship between variable Y and variable X. You hypothesize that there will be a strong positive relationship between variable Y GPA and Variable X hours of sleep. After one semester, you select five students at random out of 200 students who have taken a survey and found that they do not get more than 5 hours of sleep per night. You select five more students at random from the same survey that indicates students getting at least seven hours of sleep per night. You want to see if there is a relationship between GPA and hours of sleep. Using a Pearson Product Correlation Coefficient statistic, determine the strength and direction of the relationship and determine if you can reject or fail to reject the HO:

Variable Y        Variable X    

2.5                      5               

3.4                      8                

2.0                      4               

2.3                     4.5              

1.6                     3     

3.2                     6

2.8                     7

3.5                     7.5

4.0                     6.5

3.8                     7

solve it with exact data given not an example or other illustration.

Answer 1

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
5	2.5	0.72	0.17	0.35
8	3.4	4.62	0.24	1.05
4	2	3.42	0.83	1.68
4.5	2.3	1.82	0.37	0.82
3	1.6	8.12	1.72	3.73
6	3.2	0.02	0.08	0.04
7	2.8	1.32	0.01	-0.13
7.5	3.5	2.72	0.35	0.97
6.5	4	0.42	1.19	0.71
7	3.8	1.32	0.79	1.02

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	58.5	29.1	24.525	5.7	10.27
mean	5.85	2.91	SSxx	SSyy	SSxy

correlation coefficient ,    r = Sxy/√(Sx.Sy) =   0.8645

correlation hypothesis test      
Ho:   ρ = 0  
Ha:   ρ ╪ 0  
n=   10  
alpha,α =    0.01  
correlation , r=   0.8645  

t-test statistic = r*√(n-2)/√(1-r²) =        4.864

DF=n-2 =   8  
p-value =    0.0012  
Decison:   p value < α , So, Reject Ho  
conclusion: there is evidence that correlation coffecient is significant...