The heights (in inches) of seventh-grade girl students in a school district on L
ID: 3317496 • Letter: T
Question
The heights (in inches) of seventh-grade girl students in a school district on Long Island are known to be normally distributed. The heights of a random sample of 14 seventh-grade girl students in the school district are shown below. 8.25 57.8 64.8 61.7 59.8 62.4 68.7 57.2 57.1 63.0 66.2 58.0 62.6 57.0 60.2 a. Conduct a hypothesis test using =0.01 to show that the population mean height of the school district is lower than 63.0. Find the p-value of the test conducted in part (a) Suppose that a further study establishes that, in fact, the population mean is 61.5. Did the test in part (a) make a correct decision? If not, what type of error did it make? b. c.Explanation / Answer
a.
Given that,
population mean(u)=63
sample mean, x =61.1786
standard deviation, s =3.6826
number (n)=14
null, Ho: =63
alternate, H1: <63
level of significance, = 0.01
from standard normal table,left tailed t /2 =2.65
since our test is left-tailed
reject Ho, if to < -2.65
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =61.1786-63/(3.6826/sqrt(14))
to =-1.8506
| to | =1.8506
critical value
the value of |t | with n-1 = 13 d.f is 2.65
we got |to| =1.8506 & | t | =2.65
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value :left tail - Ha : ( p < -1.8506 ) = 0.04354
hence value of p0.01 < 0.04354,here we do not reject Ho
ANSWERS
---------------
null, Ho: =63
alternate, H1: <63
test statistic: -1.8506
critical value: -2.65
decision: do not reject Ho
b.
p-value: 0.04354
no evidence to support the claim
c.
not true when population mean is stated to 61.5
and this makes a type II error
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