What should the NULL HYPOTHESIS for this study say?

Question

You are doing a study on sleep deprivation on logical thinking. You take a sample of n = 25 individuals and deprive of them sleep so that they only get 4 hours of sleep for two nights. You then have them each solve a puzzle (this is how logical thinking is measured in this study), and find that the mean time to solve the puzzle is M = 30 minutes. You know that for the population, the mean time to solve the puzzle is μ = 10 minutes and the standard deviation is σ = 20. You want to answer the following research question: Does sleep deprivation have an effect on logical thinking?

What should the NULL HYPOTHESIS for this study say?

Answer 1

Null hypothesis: Ho: population mean of sleep deprived is 10 minutes to solve puzzle, and

sleep deprivation does not affect logical thinking

Alternative hypothesis: Ha: population mean for sleep deprived is greater than 10 minutes to solve the puzzle and sleep deprivation significantly affects logical thinking

If standard deviation is 20 minutes and sample mean is 30 minutes,

then for a 95% confidence interval, you need to be more than 2 standard deviations from the mean to reject the null hypothesis. two standard deviations is 40 minutes 30 minutes is only 20 minutes away or just one standard deviation. No one would reject the null hypothesis with standard statistical assumptions. Using less than 95% confidence intervals is not common.

conclusion, sleep deprivation does not affect logical thinking