It is believed that Lake Tahoe Community College (LTCC) Intermediate Algebra stu

Question

It is believed that Lake Tahoe Community College (LTCC) Intermediate Algebra students get more than 7 hours of sleep per night, on average. A survey of 22 LTCC Intermediate Algebra students generated a mean of 7.24 hours with a standard deviation of 1.93 hours. At a level of significance of 5%, do LTCC Intermediate Algebra students get less than 7 hours of sleep per night, on average? The Type II error is not to reject that the mean number of hours of sleep LTCC students get per night is at most seven when, in fact, the mean number of hours is les than, at least, at most or more than 7 hours? It is believed that Lake Tahoe Community College (LTCC) Intermediate Algebra students get more than 7 hours of sleep per night, on average. A survey of 22 LTCC Intermediate Algebra students generated a mean of 7.24 hours with a standard deviation of 1.93 hours. At a level of significance of 5%, do LTCC Intermediate Algebra students get less than 7 hours of sleep per night, on average? The Type II error is not to reject that the mean number of hours of sleep LTCC students get per night is at most seven when, in fact, the mean number of hours is les than, at least, at most or more than 7 hours? It is believed that Lake Tahoe Community College (LTCC) Intermediate Algebra students get more than 7 hours of sleep per night, on average. A survey of 22 LTCC Intermediate Algebra students generated a mean of 7.24 hours with a standard deviation of 1.93 hours. At a level of significance of 5%, do LTCC Intermediate Algebra students get less than 7 hours of sleep per night, on average? The Type II error is not to reject that the mean number of hours of sleep LTCC students get per night is at most seven when, in fact, the mean number of hours is les than, at least, at most or more than 7 hours?

Explanation / Answer

Given that,
population mean(u)=7
sample mean, x =7.24
standard deviation, s =1.93
number (n)=22
null, Ho: <7
alternate, H1: >7
level of significance, = 0.05
from standard normal table,right tailed t /2 =1.721
since our test is right-tailed
reject Ho, if to > 1.721
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =7.24-7/(1.93/sqrt(22))
to =0.5833
| to | =0.5833
critical value
the value of |t | with n-1 = 21 d.f is 1.721
we got |to| =0.5833 & | t | =1.721
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value :right tail - Ha : ( p > 0.5833 ) = 0.28296
hence value of p0.05 < 0.28296,here we do not reject Ho
ANSWERS
---------------
null, Ho: <=7
alternate, H1: >7
test statistic: 0.5833
critical value: 1.721
decision: do not reject Ho
p-value: 0.28296

we have evidence that the mean number of hours of sleep LTCC students get per night is at most seven

and The Type II error is not to reject that the mean number of hours of sleep LTCC students get per night is atmost sevn
in fact, the mean number of hours more than 7 hours

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