A sleep habits survey answered by 26 randomly selected New Y

A \"sleep habits\" survey answered by 26 randomly selected New Yorkers contained the question \"How much sleep do you get per night?\" The sample average was 7.8 hours, with a corresponding sample standard deviation of 0.8 hours. Conduct a hypothesis test to see if there is evidence that New Yorkers (who live, after all, in \"the city that never sleeps\") on average get less than 8 hours of sleep per night, using =0.05.

t critical value = ???_____

t test statistic = ???____
Note: Round your answer to 2 decimal precision

What is probability that we would obtain a test statistic at least this extreme if the population mean sleep time for New Yorkers was not less than 8 hours per night?  
Note: Round your answer to 4 decimal precision

At a level of significance of 0.05, the data

  ---Select--- A. provides enough...

B. Does not provide enough...

...provides enough does not provide enough evidence to suggest that New Yorkers on average get less than 8 hours of sleep per night

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   8  
Ha:    u   <   8  
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    25          
tcrit =    -1.708140761   [ANSWER, T CRITICAL]

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Getting the test statistic, as              
              
X = sample mean =    7.8          
uo = hypothesized mean =    8          
n = sample size =    26          
s = standard deviation =    0.8          
              
Thus, t = (X - uo) * sqrt(n) / s =    -1.274754878   [ANSWER, T TEST STATISTIC]

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Also, the p value is              
              
p =    0.10705854   [ANSWER, PROBABILITY]

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OPTION B: DOES NOT PROVIDE ENOUGH evidence to suggest that New Yorkers on average get less than 8 hours of sleep per night.