Show your answer by following the 5 steps in testing hypothesis.

Question

Research suggests that most people need at least 7 hours of sleep each night in order to function well the next day. Some research suggests that lack of sleep can adversely affect health, memory, learning. creativity, productivity, emotional stability, and even life expectancy. Suppose adults need 7  hours of sleep per night. You as a researcher obtained a random sample of 15 adults, and the sleeping time for each was recorded. The sample mean was 6.2 hours and assume 

the standard deviation is 0.67 hours. Is there any evidence to suggest that the mean sleeping time for adults is less than 7 hours? Use significance level = 0.05 or α=0.05. Show the steps in testing hypothesis.

Answer 1

Hi Lily,

Here's how you would solve this.

Step 1: state the null and alternative hypotheses.

H_o: µ=7 (the mean sleeping time for adults is seven hours)

H_a: µ < 7 (the mean sleeping time for adults is less than seven hours)

Step 2: Significance level of 5% (0.05), sample size n=15

Step 3: we'll be using a t-distribution since the standard deviation for all adults (the population of interest) is unknown, and we found the sample std. dev. to be 0.67 hours.

Step 4: could be done using statistical software; I used a graphing calculator for simplicity,.

The test statistic has a value of t = -4.6424. Done via this formula: (sample mean - µ) / (sample std. dev. / sqrt(sample size)) ==> (6.2-7) / (0.67/sqrt(15)). Note that the appropriate t-distribution has degrees of freedom 14 (df = n-1)

Step 5: Interpret: The test statistic of -4.62 corresponds with a p-value of 1.968*10^-4, well less than 0.05. We can reject the null hypothesis and conclude there is evidence to suggest that the true average sleeping time for adults is less than seven hours. Hope this helps!

Kris