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does using social media stress us out? Participants were randomly assigned to either use Facebook daily or to quit the social media platform entirely for 5 days. After this the participants measured a variety of measures of stress, including rating their stress on a scale from 1 (low stress) to 5 (high stress). For the participants who were to use Facebook daily the mean was 3.145 with a sum of squares equal to 3.16 (n = 10). For the participants who didn’t use Facebook for 5 days the mean was 2.478 with a sum of squares equal to 4.17 (n = 10). The data were normally distributed and the homogeneity of variance assumption was met. Use an  = .05, two tailed test.

Question

does using social media stress us out? Participants were randomly assigned to either use Facebook daily or to quit the social media platform entirely for 5 days. After this the participants measured a variety of measures of stress, including rating their stress on a scale from 1 (low stress) to 5 (high stress). For the participants who were to use Facebook daily the mean was 3.145 with a sum of squares equal to 3.16 (n = 10). For the participants who didn’t use Facebook for 5 days the mean was 2.478 with a sum of squares equal to 4.17 (n = 10). The data were normally distributed and the homogeneity of variance assumption was met. Use an  = .05, two tailed test.

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Solution

To answer this question, we need to conduct an independent samples t-test. This test is used to determine if there is a significant difference between the means of two independent groups. In this case, the two groups are those who used Facebook daily and those who didn't use Facebook for 5 days.

Here are the steps to conduct the t-test:

  1. State the hypotheses. The null hypothesis is that there is no difference in stress levels between the two groups. The alternative hypothesis is that there is a difference in stress levels between the two groups.

  2. Calculate the pooled variance. This is a weighted average of the variances of the two groups. The formula is:

    (SS1 + SS2) / (n1 + n2 - 2)

    Substituting the given values:

    (3.16 + 4.17) / (10 + 10 - 2) = 0.36625

  3. Calculate the standard error of the difference. The formula is:

    sqrt[(s^2/n1) + (s^2/n2)]

    Substituting the given values:

    sqrt[(0.36625/10) + (0.36625/10)] = 0.271

  4. Calculate the t statistic. The formula is:

    (M1 - M2) / standard error of the difference

    Substituting the given values:

    (3.145 - 2.478) / 0.271 = 2.46

  5. Determine the critical t value. For an alpha level of .05 and df = n1 + n2 - 2 = 18, the critical t value for a two-tailed test is approximately ±2.101.

  6. Compare the calculated t statistic with the critical t value. If the calculated t statistic is greater than the critical t value, reject the null hypothesis.

In this case, the calculated t statistic (2.46) is greater than the critical t value (±2.101). Therefore, we reject the null hypothesis and conclude that there is a significant difference in stress levels between those who used Facebook daily and those who didn't use Facebook for 5 days.

This problem has been solved

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