Sarah Mackay is an energetic 24 year old who likes reading, biking and dining ou

Question

Sarah Mackay is an energetic 24 year old who likes reading, biking and dining out. She wears a Fitbit which tracks her daily activities. You can find some of the Fitbit data for the summer of 2017 in the attached Excel file. Your task is to analyze some of this data and to make recommendations to Sarah. Use the Fitbit data for the following analysis.

(1) Body mass index (BMI) for a woman of less than 18.5 indicates that she is underweight. Test the null hypothesis H0 : µ = 18.5 versus the alternative H1 : µ < 18.5 at 5% level of significance. Is Sarah underweight?

(2) Experts reccomend taking at least 10,000 steps a day for an active young person. Test the null hypothesis H0 : µ = 10000 versus the alternative H1 : µ < 10000 at 5% level of significance. Based on the results of the test would you recommend to Sarah to walk more?

(3) Compute 95% confidence intervals for the minutes Sarah is Sedentary (includes sleep), Lightly Active, Fairly Active and Very Active. On average is Sarah Sedentary for more than 12 hours per day? On average is Sarah very active for less than 20 minutes per day? Longer time frame data from Sarah’s Fitbit is also available. For a sample of 200 nights this data indicates that Sarah has slept at least 8 hours on 66 of those nights. Also Sarah did not awake during sleep on 85 of these 200 nights according to the Fitbit. Use these longer term data for the rest of the analysis.

(4) Compute a 95% confidence interval for the proportion of nights Sarah sleeps at least 8 hours. Sleeping for less than 8 hours on more than half the nights is known to weaken the immune systen (besides other health effects). Based on the confidence interval you constructed would you recommend to Sarah to stress less and sleep longer?

(5) Let p be the proportion of nights Sarah sleeps through the night without waking up. Test the null hypothesis H0 : p = 0.50 versus the alternative H1 : p < 0.50 at 5% level of significance. If night sleep interupted on more than half of all nights, this leads to diminished memory recall. Sarah complains about forgeting small things all the time. What would you recommend?

Fitbit Data

BMI Calories Burned Steps Distance Floors Minutes Sedentary Minutes Lightly Active Minutes Fairly Active Minutes Very Active 17.82 2444 13377 3.91 23 1086 218 29 107 17.92 2332 16016 8.02 17 674 245 45 85 18.06 1690 7913 5.53 23 1247 163 18 12 18.07 1617 6907 4.79 22 1193 129 16 10 17.78 1218 4109 4.04 13 1054 110 10 10 17.93 2303 15136 7.13 19 846 69 13 63 18.09 1628 6490 4.5 26 855 152 16 11 17.76 1627 5933 4.12 20 603 142 21 5 17.76 1890 10623 7.37 35 832 254 16 12 17.72 2377 18608 7.55 21 859 227 65 75 17.78 1810 9368 6.5 28 883 220 23 8 17.87 1837 9390 6.55 15 1203 173 48 16 17.79 1727 8436 5.85 20 807 177 23 5 17.86 1880 11390 7.9 24 1090 214 42 12 17.89 2100 14370 4.92 30 717 151 32 87 17.77 1961 13072 9.07 24 1172 173 55 40 17.73 1926 12864 9.08 33 772 192 35 29 17.95 1823 8617 5.93 29 1201 209 12 18 17.81 1211 6790 5.07 15 1440 120 0 0 17.96 1681 6936 4.81 14 789 158 19 13 17.98 1701 7879 5.47 29 788 150 22 22 18.01 1427 2469 1.71 7 763 107 20 30 17.9 1954 12451 8.64 19 452 302 10 8 18 1807 9777 6.91 31 698 194 26 10 17.75 1754 7259 5.11 24 978 161 23 18 18.04 1898 9841 1.23 4 1321 26 14 79 18.03 1482 2536 1.76 10 676 134 6 0 18.12 1655 6827 4.74 21 1251 163 7 19 17.84 1699 8688 6.33 19 1243 161 18 18 18.11 1721 7478 5.26 18 837 173 18 18

Explanation / Answer

Q1.

using minitab:

One-Sample T: BMI

Test of mu = 18.5 vs < 18.5

95% Upper
Variable N Mean StDev SE Mean Bound T P
BMI 30 17.9033 0.1255 0.0229 17.9423 -26.04 0.000

P-value <0.05 we reject the null hypothesis. se conclude that Body mass index (BMI) for a woman of less than 18.5 indicates that she is underweight.

post remaining questions saperately.

Hope this will be helpful. Thankjsa nd God Bless you :-)

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