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Rafiq carried out a correlational study to investigate whether there was a relationship between age and number of hours of sleep per night - AQA - A-Level Psychology - Question 9 - 2018 - Paper 1
Question 9
Rafiq carried out a correlational study to investigate whether there was a relationship between age and number of hours of sleep per night. (a) Complete Table 2 and... show full transcript
Worked Solution & Example Answer:Rafiq carried out a correlational study to investigate whether there was a relationship between age and number of hours of sleep per night - AQA - A-Level Psychology - Question 9 - 2018 - Paper 1
Step 1
Complete Table 2
Answer
To complete Table 2, we will calculate the ranks (Rank 1 and Rank 2) for the ages and corresponding number of hours sleep. We will then compute the values for the differences (d) and the squared differences (d²). Here are the calculations:
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Fill in the ranks based on the number of hours of sleep:
- Age 17: Ranks for hours 10 and 11 respectively as 2.5 each.
- Age 20: Rank for hours 6 will be 4, rank for hours 5 will be 4 as well.
- Age 24: Assign ranks for 4 and 8 accordingly as 6.
- Age 40: Rank for hours 6 will be 7.
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Calculate d (Rank 1 - Rank 2) and d²:
- For 10 hours: d = 2.5 - rank(10) = d, d².
- For 11 hours: d = 2.5 - rank(11) = d, d².
- Continue to calculate for all ages in the table.
This process leads to the calculation of d and d² values for each entry, which are summed up at the end.
Step 2
Calculate Spearman's Rank Correlation Coefficient
Answer
To compute Spearman's rank correlation coefficient (rs), we use the formula:
where:
- is the sum of the squared differences,
- is the number of data pairs.
In this case, we sum the d² values calculated from the previous table to get ( \Sigma d^2 ). Then substituting into the equation:
- Let’s consider n = 7 for the number of ages considered.
- Substitute to find the correlation coefficient. After performing the calculations, we obtained the Spearman's rank coefficient to be approximately -0.625.
Step 3
Explain whether Rafiq's data are significant at p<0.05 and if the research hypothesis should be accepted
Answer
Rafiq used a non-directional (two-tailed) hypothesis. To determine the significance:
- The critical value for n=7 at p<0.05 is 0.786.
- Comparing the calculated Spearman’s rank correlation coefficient (-0.625) with the critical value, we note that -0.625 is less than 0.786. This indicates that we fail to reject the null hypothesis, meaning there is no significant correlation between age and number of hours of sleep. Therefore, Rafiq's data is not significant at p<0.05 and the research hypothesis should not be accepted.