Am I getting less than the minimum amount of sleep per night than what is recommended? This is a left-tailed question.

SPSS

Step 1. I will be analyzing the number of hours of sleep per night  that I experienced over a sample of 42 days. I collected the data using the SleepScore app on my iphone, which uses sonar sensor technology, called echolocation, to track your breathing and body movement as you travel through each sleep stage. This data, combined with your profile and lifestyle information, that you input, allows the app to track one's unique sleep patterns and overall sleep health. This is important to me because after an injury/procedure I have had much trouble being able to sleep more than 4 hours without waking up due to phantom pains and am curious about how my current sleep patterns line up with recommendations. 

Step 2. Am I getting less than the minimum amount of sleep per night than what is recommended? This is a left-tailed question.

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 Step 6.

1. My null hypothesis is that I am getting the minimum amount of sleep that is recommended  per night. In symbols, H0: μ = 8 hrs. My alternative hypothesis is that I am getting less than this amount. In symbols, Ha: μ < 8 hrs. 

1. 
   

2. α = .05

3. Assumption 1: The data is quantitative. Yes, hours of sleep per night is a ratio-level variable.

Assumption 2: The data came from a random sample. No, the data came from the nights when I just happened to bring my iphone which had the SleepScore app downloaded on it to bed. It’s possible that they are not fully representative of my “typical” nights of sleep. 

Assumption 3: The population is Normally distributed or the sample size is at least 30. Yes, not only does the population follow a fairly Normal distribution, but the sample size is 42. 

Assumption 4: The population standard deviation is unknown. Yes, I would have to know how much/many hours of sleep I’ve gotten every single night in order to calculate this.

Calculation of the test statistic, t:

1. Degrees of freedom = n - 1 = 41. Critical t-value is 1.684.

2. Because my t-statistic is further out in the left tail than my critical value, I would reject my null hypothesis. Because I am rejecting the null hypothesis, it is possible that I am making a Type I error.

3. My data suggest that I am getting fewer hours of sleep per night than the recommended average of 8 hours per night. 

Step 7.

My SPSS output matched the t statistic that I calculated by hand. My test was statistically significant (p < .001). 

Step 8. The 95% confidence interval of the difference between my average minutes of deep sleep per night and the recommended amount was (-2.57, -2.00). In other words, these data suggest that I average between 2.57 and 2 hours less than the minimum recommended 8 hours of  sleep per night. Even in the “best case” scenario, I’m getting 2 hours less than the minimum, which is why I rejected the null hypothesis in my t-test. 

Step 9. I would consider this result practically significant, because even 2 hours/night would add up quickly over the course of months or years and I would imagine have some serious health consequences (and of course, the closer I am to the worst case scenario, the more serious my sleep deficit would be). 

Step 10. My biggest limitations were (a) the fact that my sample was not random and (b) the questionable accuracy of the SleepScore app on my iphone in measuring sleep.