SOLUTION: Please help with this! I can not figure this out no matter what I do! The Sleep Foundation recommends that people get at least 8 hours of sleep every night. Based on this inform

Question 888535: Please help with this! I can not figure this out no matter what I do!
The Sleep Foundation recommends that people get at least 8 hours of sleep every night. Based on this information, your instructor feels that his students are not getting enough sleep, and claims that they are in fact getting less than the recommended 8 hours of sleep each night.
To test this, on a randomly selected day, he surveyed several classes to determine how much sleep each of his students got the night before. The following data set represents how many hours of sleep 35 randomly selected students reported on the survey from the night before:
7.3
6.0
7.8
5.5
7.3
7.8
8.4
5.3
5.3
9.9
5.5
4.1
6.7
6.9
5.4
8.6
8.5
7.3
9.3
6.8
8.0
9.8
4.3
8.2
7.9
8.7
4.9
3.0
7.9
9.7
6.6
2.5
9.7
6.7
6.1
Test your instructor's claim at a level of significance of 2% using the Classical Method:
The following parts break down the four steps of the Classical Method, which you will use for the hypothesis test in this problem:
A) State the Hypotheses
B) Determine the Test Statistic.
C) Determine the Critical Value.
D) State the conclusion. It should be in terms of the problem (give me more than just Reject Ho or Do Not Reject Ho).

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
sample mean = 6.9629
sample standard deviation = 1.9000
sample size = 35
degrees of freedom = 35 - 1 = 34
standard error = 1.9/sqrt(35) = .32116

assumed population mean is 8.
population standard deviation is not known.
use t-score rather than z-score.

t-score = (sample mean minus population mean) / standard error = (6.9629 - 8) / .32116 = -3.23

significance level of 2% for a one way confidence limit = an alpha of .02

critical t score for an alpha of .02 with 34 degrees of freedom would be plus or minus 2.13.

anything that exceeds that is statistically significant.

that means that a t score of less than -2.13 and a t score greater than +2.13 would be considered statistically significant and more then likely not due to chance variation between samples of size 35 .

the t score of the data is well beyond that and so the sample is considered statistically significant.

the probability of getting a t score less than -3.23 is .00137 which is significantly less than the significance level alpha of .02.

you would reject the null hypothesis that the average hours of sleep for the population was 8 hours or more.

even if you made this into a 2 tailed significance level, the alpha would have been .01 and the critical t factor would have been plus or minus 2.44.
-3.23 is still well below -2.44.

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