In: Statistics and Probability
A "sleep habits" survey answered by 25 randomly selected New
Yorkers contained the question "How much sleep do you get per
night?" The sample average was 7.79 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.
a. The t test statistic is:
Round your answer to 3 decimal places
b. 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?
Hint: the phrasing of this question is based on the definition of a
particular statistic. Round your answer to 3 decimal places
c. Using a level of significance of 0.05, the
data ---Select--- provides statistically significant
does not provide statistically significant evidence to suggest that
New Yorkers on average get less than 8 hours of sleep per
night.
You have one attempt for this question, so you should verify that
your answer to part b. is correct before submitting an answer to
this.
Hypotheses are:
Since population standard deviation is unknown and hypothesis test population mean so t test should be used. Here sample size is large so we can assume that sampling distribution of sample mean is normal.
Here we have following information:
So test statitics will be
Here test is left tailed and degree of freedom of the test is df=n-1=25-1=24. So for ?=0.05, critical value of the test is -1.7109.
Rejection region:
If test statistics value is lesser than -1.7109, reject the null hypothesis.
(b)
Here we need p-value. The p-value is 0.101.
(c)
Since p-value is greater than level of significance of 0.05 so we fail to reject the null hypothesis. '
The data does not provide statistically significant evidence to suggest that New Yorkers on average get less than 8 hours of sleep per night.