For the following, Use the five-step approach to hypothesis testing found on page 8-16. It states....

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

  1. State the hypothesis and identify the claim.

H0:

H1:

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

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

Variable Y        VariableX    

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 otherillustration.

Answer & Explanation Solved by verified expert
3.7 Ratings (654 Votes)

x y (x-x?)² (y-y?)² (x-x?)(y-y?)
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
?X ?Y ?(x-x?)² ?(y-y?)² ?(x-x?)(y-y?)
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:   ? = 0  
Ha:   ? ? 0  
n=   10  
alpha,? =    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 < ? , So, Reject Ho  

conclusion: there is evidence that correlation coffecient is significant...


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