Create your problem: It is reported that the average hours of sleep of all teenagers is 6.5 hours. Here is a sample of the hours of sleep of 20 random teenagers: 7.5 6 6.5 8 9 | 106.5 8| 8 67.5 9 7...

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Extracted text: Create your problem: It is reported that the average hours of sleep of all teenagers is 6.5 hours. Here is a sample of the hours of sleep of 20 random teenagers: 7.5 6 6.5 8 9 | 106.5 8| 8 67.5 9 7 6.5 || | 5 Is there enough evidence at the 5% level that the average hours of sleep of a teenager is greater than 6.5 hours? 6|6 17 Step #1: hypothesize List what is given: 5 l = 6.5 X = 7,28 N= 20 %3D X=0.05 List your Ho and Ha: Ho: l = 6.5 The average hours of sleep of a teenager is equal to 6.5 hours. Haill76.5 The average hours of sleep of a teenager is greater than 6.5 hours. Step #2: Prepare Check conditions: Condition #1: Random sample and independent → Random is stated. Condition #2: Normal- Assume is normal. Condition #3: Big population must be at least 10 times larger than the sample size. Population>10(Sample Size)→ All teenagers > 10(20) = 200 Extra by hand: lM =6.5 X=7.28 S-1.585 n= 20 SE =S = 1.585 =0.3544 20 +-X-U = Z.28-6.5=2.20 0.3544 The critical value from the t table is (df =19 at 95%): 2.09 Since our t = 2.20 the p-value would be smaller than p-value for † - 2.09 %3D


Extracted text: Create your problem: Compare your p-value to the significance level: p-value =O compared alpha 0.05. The p-valuc is smaller than alpha. Step #4: Interpret Write your conclusion: We reject Ho . There is statistically significant evidence to rejoct +Hto (p=0). We conclude the average hours of skep of teenagers is grcatar than 6.5 hours. Confidence interval: Condition #1: Random sample and independent Random is stated. Condition #2: Normal Assume is normal. Find the following: X= 7. 28 S=1.585 N= 20 +*= 2.09 又++() 7.28± 2.09(0.35H4) 7.28-0.7407 7.28 +0:7407 6.5393 8.0207 95% Confident Interval: We are 95% confident the average hours of sleep of teenagers is between 6.54 to 8.02 hours.