Does using social media stress you out? A researcher is interested in whether college students who extensively use social media tend to have higher levels of stress. To test this, a sample of nine college students were asked to fill out a survey on their stress level and provide an estimate of the number of hours they spend per day on social media. The stress survey is on a scale of \(0-100\) where higher scores are indicative of a higher level of stress. The data is given in Table 6.6.

a. Fill in the seven blank cells in Table 6.6 and describe which variable is the response variable and which variable is the predictor variable?

b. Using the data from Table 6.6, find the line of best fit.

c. Draw a scatterplot and test whether the population slope parameter is significantly different from 0 .

d. Interpret whether you believe that spending more time on social media is related to higher levels of stress.

e. Find and interpret a \(98 \%\) confidence interval for the true population slope parameter.

f. Find and interpret a \(99 \%\) confidence interval for the mean level of stress for all individuals who spend 4 hours on social media per day.

g. Find and interpret a 99\% confidence interval to predict the level of stress for an individual who spends 4 hours on social media per day.

Table 6.6

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Stress Level and Number of Hours a Random Sample of Nine Students Spend Per Day on Social Media Hours Stress (x,-x) (x-x) (yi-y) (y:-y) (x-x) (y,-y) 523 55 1.5556 2.4198 6.7778 45.9383 10.5432 40 -1.4444 -8.2222 67.6049 46 -0.4444 0.1975 -2.2222 4.9383 0.9877 4 46 0.3086 -2.2222 4.9383 -1.2346 1362 37 5.9753 -11.2222 125.9383 27.4321 46 0.1975 -2.2222 4.9383 0.9877 71 2.5556 22.7778 518.8272 38 -1.4444 2.0864 -10.2222 104.4938 14.7654 5 55 1.5556 2.4198 6.7778 45.9383 10.5432 Total 31.0000 434.0000 0.0000 22.2222 0.0000 923.5556 134.1111